WORKS   OF 
PROFESSOR  MILO   S.  KETCHUM 

PUBLISHED  BY  THE 
McGRAW-HILL  BOOK  COMPANY 


THE  DESIGN  OF  STEEL  MILL  BUILDINGS  and  the  Cal- 
culation of  Stresses  in  Framed  Structures,  Third  Edition 
Cloth,  6^x9  ins.,  pp.  562+xvi,  66  tables  and  270  illustra- 
tions in  the  text.     Price,  $4.00  net,  postpaid. 

THE  DESIGN   OF  WALLS,  BINS  AND  GRAIN  ELEVA- 
TORS, Second  Edition 

Cloth,  6^x9  ins.,  pp.  556+xiv,  40  tables,  304  illustrations 
in  the  text  and  two  folding  plates.  Price,  $4.00  net,  postpaid. 

THE  DESIGN  OF  HIGHWAY  BRIDGES  and  the  Calcula- 
tion of  Stresses  in  Bridge  Trusses 

Cloth,  6^x9  ins.,  pp.  544+xvi,  77  tables,  300  illustrations  in 
the  text  and  8  folding  plates.  Price,  $4.00  net,  postpaid. 

THE  DESIGN  OF  MINE  STRUCTURES 

Cloth,  6^x9  ins.,  pp.  46o+xvi,  65  tables,  265  illustrations 
in  the  text  and  7  folding  plates.  Price,  $4.00  net,  postpaid. 

SPECIFICATIONS  FOR  STEEL  FRAME  MILL  BUILDINGS 

Paper,  6^x9  ins.,  pp.  22.  Reprinted  from  "  The  Design  of 
Steel  Mill  Buildings."  Price,  25  cents. 

SURVEYING    MANUAL.    A   Manual  of  Field   and  Office 
Methods  for  the  Use  of  Students  in  Surveying 

By  Professors  William  D.  Pence  and  Milo  S.  Ketchum. 
Leather,  4^x7  ins.,  pp.  252  +xii,  10  plates  and  140 illustra- 
tions in  the  text.     Price,  $2.00  net,  postpaid. 

OFFICE-COPY  BOOKLET 

For  use  with  Pence  and  Ketchum's  "  Surveying  Manual." 
Tag  board,  4HX7  ins.,  pp.  32,  ruled  in  column  and  rectangles. 
Price,  $1.00  per  dozen  or  50  cents  per  half  dozen. 

Tables  of  contents  of  the  different  books  follow  the  index. 


THE  DESIGN  OF 

STEEL  MILL  BUILDINGS 

AND 

THE  CALCULATION   OF 

STRESSES  IN  FRAMED  STRUCTURES 

BY 

MILO   S.  ^ETCHUM,  C.E. 

DEAN  OF  COLLEGE  OF  ENGINEERING  AND  PROFESSOR  OF  CIVIL  ENGINEERING,  UNIVERSITY  OP 

COLORADO;   CONSULTING  ENGINEER;  MEMBER  AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS; 

MEMBER  AMERICAN  SOCIETY  FOR  TESTING  MATERIALS;   MEMBER  SOCIETY  FOR 

THE  PROMOTION  OF  ENGINEERING  EDUCATION 


THIRD  EDITION,  ENLARGED 
FIRST  THOUSAND 

TOTAL  ISSUE,   TEN   THOUSAND 


McGRAW-HILL   BOOK  COMPANY 

239   WEST   3QTH  STREET,    NEW   YORK 

6   BOUVERIE-  STREET,  LONDON,  E.  C. 

1912 


Copyright,  1903,  1906,  1912 

BY 
MILO  S.  KETCHUM 


PRESS  OP 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 


PREFACE  TO  THE   FIRST   EDITION. 


This  book  is  intended  to  provide  a  short  course  in  the  calculation 
of  stresses  in  framed  structures  and  to  give  a  brief  discussion  of  mill 
building  construction.  The  book  is  intended  to  supplement  the  elemen- 
tary books  on  stresses  on  the  one  hand,  and  the  more  elaborate  treatises 
on  bridge  design  on  the  other.  While  the  book  is  concerned  chiefly 
with  mill  buildings  it  is  nevertheless  true  that  much  of  the  matter  will 
apply  equally  well  to  all  classes  of  steel  frame  construction. 

In  the  course  in  stresses  an  attempt  has  been  made  to  give  a 
concise,  logical  and  systematic  treatment.  Both  the  algebraic  and  graphic 
methods  of  calculating  stresses  are  fully  described  and  illustrated.  Each 
step  in  the  solution  is  fully  explained  and  analyzed  so  that  the  student 
will  get  a  definite  idea  of  the  underlying  principles. 

Attention  is  called  to  the  graphic  solutions  of  the  transverse  bent, 
the  portal  and  the  two-hinged  arch,  which  are  believed  to  be  new,  and 
have  proved  their  worth  by  actual  test  in  the  class  room.  The  diagram 
for  finding  the  stress  in  eye-bars  due  to  their  own  weight  is  new,  and  its 
use  will  save  considerable  time  ii  designing  bridges. 

In  the  discussion  of  mill  building  construction  the  aim  has  been  to 
describe  the  methods  of  construction  and  the  material  used,  together 
with  a  brief  treatment  of  mill  building  design,  and  the  making  of  esti- 
mates of  weight  and  cost.  The  underlying  idea  has  been  to  give 
methods,  data  and  details  not  ordinarily  available,  and  to  discuss  the 
matter  presented  in  a  way  to  assist  the  engineer  in  making  his  designs 
and  the  detailer  in  developing  the  designs  in  the  drafting  room.  Every 
engineer  should  be  familiar  and  be  provided  with  one  or  more  of  the 
standard  handbooks,  and  therefore  only  such  tables  as  are  not  ordinarily 
available  are  given. 

254676 


iv  PREFACE. 

The  present  book  is  a  result  of  two  years  experience  as  designing 
engineer  and  contracting  agent  for  the  Gillette-Herzog  Mfg.  Co.,  Min- 
neapolis, Minn.,  and  -four  years  experience  in  teaching  the  subject  at 
the  University  of  Illinois.  This  book  represents  the  course  given  by  the 
author  in  elementary  stresses  and  in  the  design  of  metal  structures,  pre- 
liminary to  a  course  in  bridge  design.  While  written  primarily  for  the 
author's  students  it  is  hoped  that  the  book  will  be  of  interest  to  others, 
especially  to  the  younger  engineers. 

As  far  as  practicable  credit  has  been  given  in  the  body  of  the 
book  for  drawings  and  data.  In  addition  the  author  wishes  to 
acknowledge  his  indebtedness  to  various  sources  for  drawings  and 
information  to  which  it  has  not  been  practicable  to  give  proper 
individual  credit.  He  wishes  to  thank  Messrs.  C.  W.  Malcolm, 
L.  G.  Parker  and  R.  H.  Gage,  Instructors  in  Civil  Engineering  in 
the  University  of  Illinois,  for  assistance  in  preparing  the  drawings, 
especially  Mr.  Malcolm  who  made  a  large  part  of  the  drawings. 

The  author  will  consider  it  a  favor  to  have  errors  brought  to  his 
notice. 

Champaign,  111.,  M.  S.  K. 

August  17,  1903. 


PREFACE  TO  THE  SECOND   EDITION. 

In  this  enlarged  edition  more  than  100  pages  of  new  material,  in- 
cluding many  cuts,  have  been  added.  The  additions  include  a  discussion 
of  influence  diagrams ;  the  calculation  of  stresses  in  pins ;  a  chapter 
on  "  Graphic  Methods  for  Calculating  the  Deflection  of  Beams  " ;  data 
on  loads,  foundations,  and  saw-tooth  roofs ;  descriptions  of  various 
buildings ;  and  an  appendix  giving  the  analyses  of  22  Problems  in 
Graphic  Statics. 

The  author  wishes  to  acknowledge  the  appreciation  with  which 
the  first  edition  was  received  by  engineers  and  instructors. 

Boulder,  Colo.,  M.  S.  K. 

June  i,  1906. 


PREFACE  TO  THE  THIRD   EDITION. 

In  this  edition  the  chapters  on  "  Stresses  in  Framed  Structures  " 
and  "  Stresses  in  Bridge  Trusses  "  have  been  rewritten  and  enlarged ; 
the  "  Specifications  for  Steel  Frame  Buildings  "  have  been  revised  and 
rewritten;  many  of  the  cuts  in  the  book  have  been  redrawn,  and  many 
revisions  and  additions  have  been  made.  The  additions  include  two 
Problems  in  Graphic  Statics,  and  Appendix  III,  "  Structural  Drawings, 
Estimates  and  Designs/'  which  contains  78  pages,  30  tables  and  24 
cuts,  and  furnish  data  and  many  tables  not  readily  available.  The 
number  of  pages  in  this  edition  has  been  increased  by  82,  and  the  num- 
ber of  cuts  by  30. 

The  author  wishes  to  acknowledge  the  continued  appreciation  with 
which  the  book  has  been  received. 

Boulder,  Colo.,  M.  S.  K. 

June  i,  1912. 


TABLE  OF  CONTENTS. 


INTRODUCTION 

PAGE. 

Steel  Frame  Mill  Buildings i 

Steel  Mill  Buildings  with  Masonry  Filled  Walls 2 

Mill  Buildings  with  Masonry  Walls 3 

PART  I.     LOADS. 
CHAPTER  I.     DEAD  LOADS. 

Weight  of  Roof  Trusses 5 

Weight  of  Purlins,  Girts,  etc 8 

Weight  of  Covering 8 

Weight  of  Structure 9 

CHAPTER  II.     SNOW  LOADS. 

Snow  Loads 10 

CHAPTER  III.     WIND  LOADS. 

Wind  Pressure 12 

Wind  Pressure  on  Inclined  Surfaces 13 

CHAPTER  IV.     MISCELLANEOUS  LOADS. 

Live  Loads  on  Floors 17 

Weight  of  Hand  Cranes 18 

Weight  of  Electric  Cranes 18 

Weights  of  Miscellaneous  Material 19 

Concentrated  Live  Loads 21 

vii 


viii  TABLE  OF  CONTENTS 

PART  II.     STRESSES. 

CHAPTER  V.     GRAPHIC  STATICS. 

Equilibrium  22 

Representation  of  Forces 22 

Force  Triangle 22 

Force  Polygon 24 

Equilibrium  of  Concurrent  Forces 24 

Equilibrium  of  Non-concurrent  Forces 25 

Equilibrium  Polygon 26 

Reactions  of  a  Simple  Beam 29 

Reactions  of  a  Cantilever  Truss 30 

Equilibrium  Polygon  as  a  Framed  Structure 31 

Graphic  Moments   32 

Bending  Moments  in  a  Beam 33 

To  Draw  an  Equilibrium  Polygon  Through  Three  Points 33 

Center  of  Gravity 34 

Moment  of  Inertia  of  Forces 35 

Moment  of  Inertia  of  Areas 38 

CHAPTER  VI.     STRESSES  IN  FRAMED  STRUCTURES. 

Methods  of  Calculation 39 

Algebraic  Resolution 40 

Graphic  Resolution   ^2 

Algebraic  Moments 44 

Graphic  Moments 45 


CHAPTER  VII.     STRESSES  IN  SIMPLE  ROOF  TRUSSES. 

Loads  

Dead  Load  Stresses.. 


Dead  and  Ceiling  Load  Stresses 48 

Snow  Load  Stresses 49 

Wind  Load  Stresses 4O/ 

Wind  Load  Stresses :   No  Rollers 50 

Wind  Load  Stresses :  Rollers ^ 

Concentrated  Load  Stresses 


TABLE  OF  CONTENTS  ix 

CHAPTER  VIII.     SIMPLE  BEAMS. 

Reactions 55 

Moment  and  Shear  in  Beams :  Concentrated  Loads 56 

Moment  and  Shear  in  Beams :  Uniform  Loads 57 

CHAPTER  IX.     MOVING  LOADS  ON  BEAMS. 

Uniform  Moving  Loads 59 

Concentrated  Moving  Loads 61 

CHAPTER  X.     STRESSES  IN  BRIDGE  TRUSSES. 

Method  of  Loading 65 

Algebraic  Resolution 65 

Graphic  Resolution 70 

Algebraic  Moments 72 

Graphic  Moments 73 

Wheel   Loads 76 

Influence  Diagrams 77 

Maximum  Moment  in  a  Truss 77 

Maximum  Shear  in  a  Truss 79 

Maximum  Floor  Beam  Reaction 81 

CHAPTER  XI.     STRESSES  IN  A  TRANSVERSE  BENT. 

Dead  and  Snow  Load  Stresses 83 

Wind  Load  Stresses 83 

Algebraic  Calculation  of  Stresses : 

Case  I.  Columns  Hinged  at  the  Base 84 

Case  II.  Columns  Fixed  at  the  Base 87 

Maximum  Stresses 91 

Stresses  in  End  Framing 92 

Bracing  in  the  Upper  Chord  and  Sides 92 

Graphic  Calculation  of  Stresses : 

Data 93 

Case  i.  Permanent  Dead  and  Snow  Load  Stresses 94 

Case  2.  Wind  Load  Stresses ;  Wind  Horizontal ;  Columns 

Hinged    0,6 

Case  3.  Wind  Load  Stresses ;  Wind  Horizontal ;  Columns 

Fixed  at  Base 98 


x  TABLE  OF  CONTENTS 

Case  4.  Wind   Load   Stresses ;   Wind   Normal ;   Columns 

Hinged 99 

Case  5.  Wind   Load   Stresses ;   Wind   Normal ;   Columns 

Fixed  at  Base 101 

Maximum  Stresses ; IO1 

Graphic  Calculation  of  Reactions • 103 

Transverse  Bent  with  Ventilator 103 

Transverse  Bent  with  Side  Sheds 105 

CHAPTER  XII.     STRESSES  IN  PORTALS. 

Introduction   IO9 

Case  I.  Stresses  in  Simple  Portals:   Columns  Hinged. 

Algebraic  Solution no 

Graphic  Solution 1 12 

Simple  Portal  as  a  Three-hinged  Arch 1 14 

Case  II.  Stresses  in  Simple  Portals :   Columns  Fixed. 

Algebraic  Solution 115 

Anchorage  of  Columns : 115 

Graphic  Solution 117 

Stresses  in  Continuous  Portals 117 

Stresses  in  a  Double  Portal. 118 

CHAPTER  XIII.     STRESSES  IN  THREE-HINGED  ARCH. 

Introduction   120 

Calculation  of  Stresses 120 

Calculation  of  Reactions :  Algebraic  Method 120 

Calculation  of  Reactions :   Graphic  Method 121 

Calculation  of  Dead  Load  Stresses 122 

Calculation  of  Wind  Load  Stresses 125 

CHAPTER  XIV.    STRESSES  IN  TWO-HINGED  ARCH. 

Introduction   127 

Calculation  of  Stresses 127 

Calculation  of  the  Reactions 128 

Algebraic  Calculation  of  Reactions. 131 

Graphic  Calculation  of  Reactions 133 


TABLE  OF  CONTENTS  xi 

Calculation  of  Dead  Load  Stresses  in  Arch 135 

Dead  and  Wind  Load  Stresses  in  Arch 137 

Arch  with  Horizontal  Tie 139 

Temperature  Stresses 140 

Design  of  Two-hinged  Arch 141 

CHAPTER  XV.     COMBINED  AND  ECCENTRIC  STRESSES. 

Combined  Direct  and  Cross  Bending  Stresses 143 

Combined  Compression  and  Cross  Bending 145 

Combined  Tension  and  Cross  Bending 148 

Stress  in  a  Bar  Due  to  its  Own  Weight 149 

Diagram  for  Stress  in  Bars  Due  to  Their  Own  Weight 149 

Eccentric  Riveted  Connections 152 

Stresses  in  Pins 154 

CHAPTER  XV A.     GRAPHIC  METHODS  FOR  CALCULATING  THE  DEFLEC- 
TION OF  BEAMS. 

Introduction    158 

Graphic  Equation  of  the  Elastic  Curve 158 

Simple  Beam   161 

Cantilever  Beam 162 

Continuous  Beams 164 

Continuous  Beam  of  n  Spans 168 

Transverse   Bent 168 

Reactions  of  Simple  Draw  Bridges 169 

Draw  Bridge  with  Three  Supports 170 

Draw  Bridge  with  Four  Supports 172 


PART  III.     DESIGN  OF  MILL  BUILDINGS.       , 

CHAPTER  XVI.     GENERAL  DESIGN. 
General  Principles 175 

CHAPTER  XVII.     FRAMEWORK. 

Arrangement 179 

Trusses — Types  of  Trusses 180 

Saw  Tooth  Roofs..  .181 


xii  TABLE  OF  CONTENTS 

Ketchum's  Saw  Tooth  Roof 186 

Pitch  of  Roof I91 

Pitch  of  Truss I92 

Economic  Spacing  of  Trusses I92 

Transverse  Bents 195 

Truss  Details   IQ7 

Columns 202 

Column  Details 205 

Struts  and  Bracing 211 

Purlins  and  Girts 213 

Design  of  Parts  of  the  Structure 213 

Design  of  Trusses 214 

Design  of  Columns. 217 

Design  of  Plate  Girders 221 

Crane  Girders 224 

CHAPTER  XVIII.     CORRUGATED  STEEL. 

Introduction    225 

Fastening  Corrugated  Steel 227 

Strength  of  Corrugated  Steel 230 

Corrugated  Steel  Details . . .  . 232 

Anti-condensation  Roofing 241 

Corrugated  Steel  Plans 244 

Cost  of  Corrugated  Steel 244 

CHAPTER  XIX.    ROOF  COVERINGS. 

Introduction    246 

Corrugated  Steel  Roofing 246 

Slate  Roofing 247 

Tile  Roofing 250 

Tin  Roofs . 251 

Sheet  Steel  Roofing 253 

Gravel  Roofing 254 

Slag  Roofing 256 

Asphalt  Roofing 257 

Shingle  Roofs 258 

Asbestos  Roofing 258 


TABLE  OF  CONTENTS  xiii 

Carey's  Roofing 259 

Granite  Roofing 259 

Ruberoid  Roofing 259 

Ferroinclave 260 

Examples  of  Roofs 261 

Roof  Coverings  for  Railway  Buildings 261 

CHAPTER  XX.     SIDE  WALLS  AND  MASONRY  WALLS. 

Side  Walls . 263 

Corrugated  Steel 263 

Expanded  Metal  and  Plaster 263 

Concrete  Slabs 266 

Masonry  Walls 267 

Concrete  Buildings 268 

CHAPTER  XXI.     FOUNDATIONS. 

Bearing  Power  of  Soils 272 

Bearing  Power  of  Piles 273 

Pressure  of  Wall  on  Foundation 275 

Pressure  of  Pier  on  Foundation 277 

Design  of  Footings 278 

Pressure  of  Column  on  Masonry 278 

Allowable  Pressures 279 

CHAPTER  XXII.     FLOORS. 

Ground  Floors — Types  of  Floors 281 

Cement  Floors  282 

Tar  Concrete  Floors 284 

Brick  Floors 284 

Wooden  Floors 285 

Examples  of  Floors 288 

Floors  above  Ground 290 

Timber  Floors 290 

Brick  Arch  290 

Corrugated  Iron  Arch 291 

Expanded  Metal 292 


xiv  TABLK  OF  CONTENTS 

Roebling 293 

"  Buckeye  "  Fireproof 294 

Multiplex  Steel 295 

Ferroinclave   295 

Corrugated    295 

Buckled  Plates 296 

Steel  Plate 297 

Thickness  of  Timber  Flooring 297 


CHAPTER  XXIII.    WINDOWS  AND  SKYLIGHTS. 

Glazing   298 

Glass 298 

Diffusion  of  Light 299 

Relative  Value  of  Different  Kinds  of  Glass 301 

Kind  of  Glass  to  Use 301 

Placing  the  Glass 302 

Use  of  Window  Shades 303 

Size  and  Cost  of  Glass 304 

Cost  of  Windows 305 

Translucent  Fabric  306 

Cost  of  Translucent  Fabric 307 

Double  Glazing 307 

Details  of  Windows  and  Skylights 307 

Amount  of  Light  Required 310 

Skylights  for  Trainsheds 315 

CHAPTER  XXIV.     VENTILATORS. 

Ventilators 317 

Monitor  Ventilators  . . 317 

Cost  of  Monitor  Ventilators 320 

Circular  Ventilators 320 

CHAPTER  XXV.    DOORS. 

Paneled  Doors 322 

Wooden  Doors ' 322 

Steel  Doors 323 

Cost  of  Doors 325 


TABLE  OF  CONTENTS  xv 

CHAPTER  XXVI.     SHOP  DRAWINGS  AND  RULES. 

Shop  Drawings 326 

Erection  Plan 327 

Choice  of  Sections 328 

CHAPTER  XXVII.     PAINTS  AND  PAINTING. 

Corrosion  of  Steel   330 

Paint    330 

Oil  Paint 330 

Linseed  Oil 331 

Lead 332 

Zinc   333 

Iron  Oxide 333 

Carbon ' : 333 

Mixing  the  Paint 334 

Proportions 334 

Covering  Capacity 334 

Applying  the  Paint 335 

Cleaning  the  Surface 336 

Cost  of  Paint 336 

Cost  of  Painting 337 

Priming  Coat 337 

Finishing  Coat 338 

Asphalt  Paint 339 

Coal-Tar  Paint 339 

Cement  and  Cement  Paint 339 

Portland  Cement  Paint 340 

References  on  Paint  and  Painting 340 

CHAPTER  XXVIII.     ESTIMATE  OF  WEIGHT  AND  COST 

Estimate  of  Weight 341 

Estimate  of  Cost 349 

Cost  of  Material 350 

Cost  of  Mill  Details 350 

Shop  Cost 353 

Cost  of  Drafting 354 

Actual  Shop  Costs 355 

Cost  of  Erection 355 

Cost  of  Miscellaneous  Material 355 


xvi  TABLE  OF  CONTENTS 

PART  IV.     MISCELLANEOUS  STRUCTURES. 

Steel  Dome  for  West  Baden,  Ind.,  Hotel 359 

The  St.  Louis  Coliseum 362 

The  Locomotive  Shops  of  the  Atchison,  Topeka  and  Santa  Fe  R.  R.  367 
The  Locomotive   Erecting  and   Machine   Shop,   Philadelphia  and 

Reading  R.  R 372 

The  New  Steam  Engineering  Building  for  the  Brooklyn  Navy  Yard.38i 

Government  Building,  St.  Louis  Exposition 385 

Reinforced  Concrete  Round-house  for  Canadian  Pacific  Railway . .  .  388 

APPENDIX  I. 
Specifications  for  Steel  Frame  Mill  Buildings 391 

APPENDIX  II. 

Problems  in  Graphic  Statics  and  the  Calculation  of  Stresses 423 

Index    473 

APPENDIX  III. 

Structural  Drawings,  Estimates  and  Designs. 

Chapter      I.     Plans  of  Structures 2 

Chapter    II.     Structural  Drawings    3 

Chapter  III.     Estimates  of  Structural  Steel   32 

Chapter  IV.     Design  of  Steel  Structures 44 

Chapter    V.     Tables  and  Structural  Standards 48 


STEEL  MILL  BUILDINGS 


INTRODUCTION. 

Steel  mill  buildings  may  be  divided  into  three  classes  as  follows: 
(i)  steel  frame  mill  buildings;  (2)  steel  mill  buildings  with  masonry 
filled  walls;  and  (3)  mill  buildings  with  masonry  walls. 

i.  Steel  Frame  Mill  Buildings. — A  steel  frame  mill  building 
is  made  by  covering  a  self-supporting  steel  frame  with  a  light  covering, 
usually  fireproof.  The  framework  consists  of  transverse  bents  firmly 
braced  by  purlins,  girts  and  diagonal  braces.  The  usual  methods  of 
arranging  the  framework  are  as  shown  in  Fig.  I. 


fc) 


FIG.  i. 


An  intermediate  transverse  bent  (c),  Fig.  I,  consists  of  a  steel 
roof  truss  with  its  ends  supported  on  steel  posts,  and  is  made  rigid  by 
knee  braces.  The  posts  are  either  supported  on  the  foundations  or  are 
anchored  by  them.  The  end  bents  are  made  either  by  running  the  end 
posts  up  to  the  end  rafters  as  in  (a),  or  by  means  of  an  end  trussed 
bent  as  in  (b)  Fig.  i.  The  end  trussed  bent  (b)  is  usually  preferred 
where  extensions  are  contemplated,  although  the  end  post  bent  (a)  is 
equally  satisfactory  and  is  usually  somewhat  cheaper. 


2    '  '"^  INTRODUCTION 

The  building  is  firmly  braced  transversely  by  means  of  bracing  in 
the  planes  of  the  upper  and  lower  chords  and  in  the  end  bents,  and 
longitudinally  by  means  of  bracing  in  the  sides  and  in  the  planes  of  the 
upper  and  lower  chords. 

The  roof  covering  is  supported  on  steel  purlins  placed  at  right 
angles  to  the  trusses  and  rafters.  The  side  covering  is  fastened  to 
horizontal  girts  which  are  fastened  to  the  side  and  end  posts.  Where 
warmth  is  desired  the  roof  and  sides  are  lined. 

Steel  frame  mill  buildings  are  usually  covered  with  corrugated 
iron  or  steel  fastened  to  sheathing  or  directly  to  the  purlins  and  girts. 
Expanded  metal  and  plaster,  or  wire  netting  and  plaster  has  been  used 
to  a  limited  extent  for  covering  the  sides  and  for  sheathing  the  roof, 
and  will  certainly  be  much  used  in  the  future  where  permanent  struct- 
ures are  required.  In  the  latter  case  slate  or  tile  roofing  is  commonly 
used. 

The  buildings  are  lighted  by  means  of  windows  in  the  side  walls 
and  the  clerestory  of  the  monitor  ventilator  shown  in  Fig.  i,  or  by 
means  of  windows  in  the  side  walls  and  skylights  in  the  roof.  Ventila- 
tion is  effected  by  means  of  the  monitor  ventilator  shown  in  Fig.  I  or 
by  means  of  circular  ventilators.  Where  glass  is  used  in  the  clere- 
story of  monitor  ventilators  the  sash  are  made  movable.  The  glass  in 
the  clerestory  of  monitor  ventilators  is  often  replaced  by  louvres  which 
allow  a  free  circulation  of  air  and  keep  out  the  storm.  In  foundries  and 
smelters  the  clerestory  is  often  left  entirely  open  or  is  slightly  protected 
by  simple  swinging  shutters. 

2.  Steel  Mill  Buildings  with  Masonry  Filled  Walls.— In  mill 
buildings  of  this  type  part  of  the  bracing  in  the  side  walls  is  usually 
omitted  and  the  space  between  the  columns  is  filled  with  a  light  wall  of 
brick,  stone,  concrete  or  hollow  tile.  The  construction  of  the  roof  and 
other  constructional  details  are  essentially  the  same  as  for  steel  frame 
mill  buildings.  Buildings  of  this  type  are  quite  rigid  and  are  usually 
somewhat  cheaper  than  type  (3). 


TYPES  OF  MILL  BUILDINGS  3 

3.  Mill  Buildings  with  Masonry  Walls. — Buildings  of  this 
type  are  made  by  supporting  the  roof  trusses  directly  on  brick,  stone 
or  concrete  walls.  The  construction  of  the  roof  is  essentially  the  same 
as  for  types  (i)  and  (2),  except  that  the  trusses  are  somewhat  lighter 
on  account  of  the  smaller  wind  stresses. 

The  discussion  of  the  simple  steel  frame  mill  building  shown  in 
Fig.  i  includes  practically  all  the  problems  and  details  which  are  en- 
countered in  the  design  of  steel  mill  buildings  of  all  types. 

The  problems  involved  in  the  design  of  mill  buildings  will  be  di- 
vided into  Part  I,  Loads ;  Part  II,  Stresses ;  Part  III,  Design  of  Mill 
Buildings;  and  Part  IV,  Miscellaneous  Structures.  In  general  the 
discussion  will  relate  to  the  design  of  mill  buildings  but  in  a  few  cases, 
particularly  in  stresses,  quite  a  number  of  problems  will  be  discussed 
that  are  only  indirectly  related  to  the  subject. 


PART  1. 

LOADS. 

The  loads  to  be  provided  for  in  designing  a  mill  building  will  de- 
pend to  a  large  degree  upon  the  use  to  which  the  finished  structure  is 
to  be  put.  The  loads  may  be  classed  under  (i)  dead  loads;  (2)  snow 
loads;  (3)  wind  loads;  and  (4)  miscellaneous  loads.  Concentrated  floor 
and  roof  loads,  girder  and  jib  crane,  arid  miscellaneous  loads  should 
receive  special  attention,  and  proper  provision  should  be  made  in  each 
case.  No  general  solution  can  be  given  for  providing  for  miscellaneous 

loads,  but  each  problem  must  be  worked  out  to  suit  local  conditions. 

* 


CHAPTER  I. 
DEAD  LOADS. 

Dead  loads  may  be  divided  into  (a)  weight  of  structure ;  (b)  con- 
centrated loads. 

The  weight  of  the  structure  may  be  divided  into  (i)  the  weight 
of  the  roof  trusses;  (2)  the  weight  of  the  roof  covering;  (3)  the  weight 
of  the  purlins  and  bracing;  (4)  the  weight  of  the  side  and  end  walls. 
The  first  three  items,  together  with  the  concentrated  roof  loads,  consti- 
tute the  dead  loads  used  in  designing  the  trusses. 

The  weights  of  mill  buildings  vary  so  much  that  it  is  not  possible 
to  give  anything  more  than  approximate  values  for  the  different  items 
which  go  to  make  up  the  dead  load.  The  following  data  will,  however, 
materially  assist  the  designer  in  arriving  at  approximately  the  proper 


WEIGHT  OF  ROOF  TRUSSES  5 

dead  load  to  assume  for  computing  stresses,  and  the  approximate  weight 
of  metal  to  use  as  a  basis  for  preliminary  estimates. 

Weight  of  Roof  Trusses.  —  The  weight  of  roof  trusses  varies 
with  the  span,  the  distance  between  trusses,  the  load  carried  or  capacity 
of  the  truss,  and  the  pitch. 

The  empirical  formula 


where 

£Fr=weight  of  steel  roof  truss  in  pounds; 

P=capacity  of  truss  in  pounds  per  square  foot  of  horizontal  pro- 
jection of  roof  (30  to  So  Ibs.)  ; 

^=distance  center  to  center  of  trusses  in  feet  (8  to  30  feet)  ; 

Z,=span  of  truss  in  feet; 

was  deduced  by  the  author  from  the  computed  and  shipping  weights 
of  mill  building  trusses.  The  trusses  were  riveted  Fink  trusses  with 
purlins  placed  at  panel  points,  and  were  made  up  of  angles  with  con- 
necting plates  ;  minimum  size  of  angles  2"  x  2"  x  J4",  minimum  thick- 
ness of  plates  ,J4". 

The  trusses  whose  weights  were  used  in  deducing  this  formula  had 
a  pitch  of  Y$  (6"  in  12"),  but  the  formula  gives  quite  accurate  results 
for  trusses  having  a  pitch  of  %  to  ^.  The  trusses  were  designed 
for  a  tensile  stress  of  15000  Ibs.  per  square  inch  and  a  compressive 

stress  of  15000  —  55  —Ibs.  per  square  inch,  where  /  =  length  and  r  — 

the  radius  of  gyration  of  the  member,  both  in  inches. 

The  weight  of  steel  roof  trusses  for  a  capacity,  P,  of  40  Ibs.  per 
square  foot  for  different  spacings  is  given  in  Fig.  2.  The  weights  of 
trusses  for  other  capacities  can  be  obtained  by  multiplying  the  tabular 
values  by  the  ratio  of  the  capacities. 

Dividing  (i)  by  A  L  we  have  the  weight  of  roof  truss,  W  s,  per 
square  foot  of  horizontal  projection  of  the  roof 

w  -  —  (n    L  ~) 

ty'~          L  +  (2) 


6 


DEAD  LOADS 


10000 

£  9000 
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keooo 
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General  Formula 

for 

Weight  of  Roof  Trusses 


tV=weightof  truss  in  Ibs 
/^capacity of  roof  in  Ibs  persq-ft 
A=  distance  between  trusses  in  ft 
L=  span  of  truss  in  ft- 
Pitch  of  roof  =i(6"in  12") 


Compression    I5000-55rlbspersqi 

Tension      1 5000  Ibs  per  sq-in- 

Rtch=i(6"ml2") 


20 


90 


IOO 


30         4-0  50          6O  70          80 

Lenqth  of  Span  of  Truss  Z.,  Ft- 

FIG.  2.    WEIGHT  OF  ROOF  TRUSSES  FOR  A  CAPACITY  OF  40  LBS.  PER 

SQUARE  FOOT. 

The  weight  of  steel  roof  trusses  per  square  foot  of  horizontal 
projection  of  roof  for  a  capacity,  Pf  of  40  Ibs.  per  square  foot  is  giveg 
in  Fig  3. 

It  should  be  noted  that  W  B  is  the  dead  load  per  square  foot  carried 
by  an  interior  truss.  The  actual  weight  of  trusses  per  square  foot  of 

horizontal  projection  for  a  building  with  n  panels  will  be  W 's   ii 

where  end  post  bent  (a),  Fig.  i,  is  used,  and  Ws  ^  *"    •)   where  end 

truss  bent  (b),  Fig.  i,  is  used,  assuming  that  all  trusses  are  made  alike. 

Weight  of  Light  Trusses. — Formula  (i)  gives  the  weight  of  mill 

building  trusses  and  will  usually  cover  the  weight  of  knee  braces  and 

ventilator  framing.    By  reducing  the  minimum  thickness  of  metal  and 


WEIGHT  OF  ROOF  TRUSSES 


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Length  of  Span  of  Truss, L,  in  feet- 

FIG.    3.    WEIGHT  OF  ROOF  TRUSSES  PER  SQUARE  FOOT  OF  HORIZONTAL 

PROJECTION  FOR  A  CAPACITY  OF  40  LBS.  PER  SQUARE  FOOT. 

by  skinning  the  sections  it  is  possible  to  materially  reduce  the  weights. 
Weight  of  Simple  Roof  Trusses. — Simple  roof  trusses  supported 


TABLE  I. 

WEIGHT  OF  FINK  TRUSSES,  SUPPORTED  ON  MASONRY  WALLS,  DE- 
SIGNED FOR  A  VERTICAL  LOAD  OF  40  POUNDS  PER  SQUARE  FOOT  OF 
HORIZONTAL  PROJECTION  OF  ROOF. 


Span,  L, 
in  Feet 

Distance 
between 
Trusses.  A, 
in  Feet 

Weight  of 
Truss,  W, 
in  Pounds 

Span,  L, 
in  Feet 

Distance 
between 
Trusses,  A, 
in  Feet 

Weight  of 
Truss,  W. 
in  Pounds 

30 

16 

741 

65 

20 

3226 

30 

14 

621 

70 

20 

3951 

35 

16 

910 

75 

20 

4564 

40 

16 

1211 

75 

14 

3200 

40 

14 

976 

80 

20 

5160 

45 

16 

1423 

85 

25 

6730 

50 

16 

1865 

85 

14 

4000 

50 

14 

1550 

90 

25 

8010 

55 

16 

2103 

95 

25 

8600 

60 

20 

2870 

100 

25 

9392 

60 

14 

2120 

8 


DEAD  LOADS 


on  walls  will  usually  weigh  somewhat  less  than  the  value  given  by 
Formula  ( I ) .  The  computed  weights  of  Fink  roof  trusses  without  ven- 
tilators and  with  purlins  spaced  from  4  to  8  feet  are  given  in  Table  I. 

These  trusses  were  designed  by  two  different  bridge  companies  to 
serve  as  standards  and  represent  minimum  weights.  The  trusses  with  a 
spacing  of  14  feet  were  designed  with  minimum  thickness  of  metal  3-16" 
and  minimum  size  of  angles  2"  x  i^"  x  3-16".  In  the  remainder 
of  the  trusses  the  minimum  thickness  of  plates  was  *4"  and  minimum 
size  of  angles  2"  x  2"  x  %" '.  The  trusses  are  all  too  light  to  give  good 
service  although  their  use  in  temporary  structures  may  sometimes  be 
allowable. 

Weight  of  Purlins,  Girts,  Bracing,  and  Columns. — Steel 
purlins  will  weigh  from  \]/2  to  4  pounds  per  square  foot  of  area  covered, 
depending  upon  the  spacing  and  the  capacity  of  the  trusses  and  the 
snow  load.  If  possible  the  actual  weight  of  the  purlins  should  be  cal- 
culated. Girts  and  window  framing  will  weigh  from  1 54  to  3  pounds 
per  square  foot  of  net  surface.  Bracing  is  quite  a  variable  quantity. 
The  bracing  in  the  planes  of  the  upper  and  lower  chords  will  vary  from 
YZ  to  I  pound  per  square  foot  of  area.  The  side  and  end  bracing,  eave 
struts  and  columns  will  weigh  about  the  same  per  square  foot  of  sur- 
face as  the  trusses. 

Weight  of  Covering. — The  weight  of  corrugated  iron  or  steel 
covering  varies  from  1^2  to  3  pounds  per  square  foot  of  area. 

WEIGHT  OF  FLAT  AND  CORRUGATED  STEEL  SHEETS  WITH  2^/2   INCH 

CORRUGATIONS. 


Thickness 

Weight     per     Sc 

uare   (  100  sq-tT-) 

Gaqe  No. 

in 

Flat  Sheets 

Corrugated  Sheets 

inches 

Black 

Galvanized 

Black  Painted 

Galvanized 

16 

.0625 

250 

266 

275 

191 

Id 

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aOO 

2/6 

220 

256 

ao 

•0373 

150 

166 

165 

Ida 

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24 

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too 

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III 

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^6 

-0/88 

75 

91 

84- 

99 

ad 

•0/36 

65 

79 

69 

66 

WEIGHT  OF  ROOT?  COVERING  9 

In  estimating  the  weight  of  corrugated  steel  allow  about  25  per  cent 
for  laps  where  two  corrugations  side  lap  and  6  inches  end  lap  are  re- 
quired, and  about  15  per  cent  for  laps  where  one  corrugation  side  lap 
and  4  inches  end  lap  are  required.  Nos.  20  and  22  corrugated  steel 
are  commonly  used  on  the  roof  and  Nos.  22  and  24  on  the  sides. 

Weight  of  Roof  Covering. — The  approximate  weight  per  square 
foot  of  various  roof  coverings  is  given  in  the  following  table : 

Corrugated  iron,  without  sheathing I  to     3       Ibs. 

Felt  and  asphalt,  without  sheathing 2 

Felt  and  gravel,  without  sheathing 8  to  10 

Slate,  3-16"  to  %",  without  sheathing 7  to     9 

Tin,  without  sheathing  I  to     il/2     " 

Skylight  glass,  3-16"  to  %",  including  frames  4  to  10 

White  pine  sheathing  i"  thick   3 

Yellow  pine  sheathing  i"  thick 4 

Tiles,  flat 15  to  20 

Tiles,  corrugated    . .  8  to  10 

Tiles,  on  concrete  slabs 30  to  35 

Plastered  ceiling 10 

For  additional  data  on  weight  of  roof  coverings,  see  Chapter  XIX. 

The  actual  weight  of  roof  coverings  should  be  calculated  if  possible. 

Weight  of  the  Structure. — The  weight  of  the  roof  can  now  be 

fcund.    The  weight  of  the  steel  in  the  sides  and  ends  is  approximately 

the  same  per  square  foot  as  the  steel  work  in  the  roof. 

A  very  close  approximation  to  the  weight  of  the  steel  in  the  en- 
tire structure  where  no  sheathing  is  used  and  the  same  weight  of  cor- 
rugated iron  is  used  on  sides  as  on  roof,  may  be  found  as  follows: 
Take  the  sum  of  the  horizontal  projection  of  the  roof  and  the  net  sur- 
face of  the  sides  and  ends,  after  subtracting  one-half  of  the  area  of  the 
windows,  wooden  doors  and  clear  openings ;  multiply  the  sum  of  these 
areas  by  the  weight  per  square  foot  of  the  horizontal  projection  of  the 
roof,  and  the  product  will  be  the  approximate  weight  of  the  steel  in 
the  structure. 


CHAPTER  II. 
SNOW  LOADS. 

The  annual  snowfall  in  different  localities  is  a  function  of  the 
humidity  and  the  latitude  and  is  quite  a  variable  quantity.  The  amount 
of  snow  on  the  ground  at  one  time  is  still  more  variable.  In  the  Lake 
Superior  region  very  little  of  the  snow  melts  as  it  falls,  and  almost  the 
entire  annual  snowfall  is  frequently  on  the  ground  at  one  time;  while 
on  the  other  hand  in  the  same  latitude  in  the  Rocky  Mountains  the  dry 
winds  evaporate  the  snow  in  even  the  coldest  weather  and  a  less  pro- 
portion accumulates.  In  latitudes  of  35  to  45  degrees  the  heavy  snow- 
falls are  often  followed  by  a  sleeting  rain,  and  the  snow  and  ice  load 
on  roofs  sometimes  nearly  equals  the  weight  of  the  annual  snowfall. 

From  the  records  of  the  snowfall  for  the  past  ten  years  as  given 
ir  the  reports  of  the  U.  S.  Weather  Bureau  and  data  obtained  by 
personal  experience,  in  British  Columbia,  Montana,  the  Lake  Superior 
region  and  central  Illinois  the  author  presents  the  values  given  in  Fig. 
4  for  snow  loads  for  roofs  of  different  inclinations  in  different  latitudes. 
For  the  Pacific  coast  and  localities  with  low  humidity,  take  one-half 
of  the  values  given.  The  weight  of  newly  fallen  snow  was  taken  at  5 
Ibs.  and  packed  snow  at  12  Ibs.  per  cubic  foot. 

A  high  wind  may  follow  a  heavy  sleet  and  in  designing  the  trusses 
the  author  would  recommend  the  use  of  a  minimum  snow  and  ice  load 
as  given  in  Fig.  4  for  all  slopes  of  roofs.  The  maximum  stresses  due 
to  the  sum  of  this  snow  load,  the  dead  and  wind  loads ;  the  dead  and 
the  wind  loads ;  or  of  the  maximum  snow  load  and  the  dead  load  be- 
ing used  in  designing  the  members. 


Sxow  LOAD  ON  ROOFS 


II 


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Latitude  in  Degrees 


50 


FlG.    4.      SNOW    LOAD    ON    ROOFS    FOR    DIFFERENT    LATITUDES,    IN    LBS. 

PER   SQUARE  FOOT. 

Snow  loads  per  square  foot  o*  horizontal  projection  of  roof  are 
specified  in  various  localities  as  follows:  Chicago  and  New  York,  20 
Ibs. ;  Cincinnati  and  St.  Louis,  10  Ibs. ;  New  England,  30  Ibs.  The 
Baltimore  and  Ohio  Railroad  specifies  20  Ibs.  per  square  foot  of  hori- 
zontal projection  of  roof. 


CHAPTER  III. 
WIND  LOADS. 

Wind  Pressure. — The  wind  pressure  (P)  in  pounds  per  square 
foot  on  a  flat  surface  normal  to  the  direction  of  the  wind  for  any  given 
velocity  (F)  in  miles  per  hour  is  given  quite  accurately  by  the  formula 

P  =  0.004  F2  (3) 

The  following  table  gives  the  pressure  per  square  foot  on  a  flat 
surface  normal  to  the  direction  of  the  wind  for  different  velocities  as 
calculated  by  formula  (3). 

Vel.  in  miles         Pressure,  Ibs.  per 
per  hour.  square  foot. 

10 0.4 Fresh  breeze. 

20 1.6 

30 3.6 Strong  wind. 

40 6.4 High  wind. 

50 10. o Storm. 

60 14.4 Violent  storm. 

80 25.6 Hurricane. 

ioo 40.0 Violent  hurricane. 

The  pressure  on  other  than  flat  surfaces  may  be  taken  in  per  cents 
of  that  given  by  formula  (3)  as  follows :  80  per  cent  on  a  rectangular 
building;  60  per  cent  on  the  convex  side  of  cylinders;  115  to  130  per 


WIND  PRESSURE  13 

cent  on  the  concave  side  of  cylinders,  channels  and  flat  cups ;  and  130 
to  170  per  cent  on  the  concave  sides  of  spheres  and  deep  cups. 

The  pressure  on  tne  vertical  sides  of  buildings  is  usually  taken  at 
30  pounds  per  square  foot,  equivalent  to  P  equals  37^  pounds  in 
formula  (3).  This  would  give  a  "velocity  of  96  miles  per  hour,  which 
would  seem  to  be  sufficient  for  all  except  the  most  exposed  positions 
The  velocity  of  the  wind  in  the  St.  Louis  tornado  was  about  120  miles 
per  hour.  The  records  of  the  U.  S.  Weather  Bureau  for  the  last  ten 
years  show  only  one  instance  where  the  velocity  of  the  wind  as  recorded 
by  the  anemometer  was  more  than  90  miles  per  hour.  The  actual  pres- 
sure of  wind  gusts  has  been  found  to  be  about  60  per  cent  and  the 
actual  steady  wind  pressure  only  about  36  per  cent  of  that  registered  by 
ordinary  small  anemometers,  which  further  reduces  the  intensity  of  the 
observed  pressures.  The  wind  pressure  has  been  found  to  increase 
as  the  distance  above  the  ground  increases. 

Recent  German  specifications  for  design  of  tall  chimneys  specify 
wind  loads  per  square  foot  as  follows:  26  pounds  on  rectangular 
chimneys ;  67  per  cent  of  26  pounds  on  circular  chimneys ;  and  7 1  per 
cent  of  26  pounds  on  octagonal  chimneys. 

The  building  laws  of  New  York,  Boston  and  Chicago  require  that 
steel  buildings  be  designed  for  a  horizontal  wind  pressure  of  30  pounds 
per  square  foot.  The  Baltimore  and  Ohio  Railroad  specifies  a  horizon- 
tal wind  pressure  of  30  pounds  per  square  foot. 

From  the  above  discussion  it  would  seem  that  30  pounds  per  square 
foot  on  the  sides  and  the  normal  component  of  a  horizontal  pressure  of 
30  pounds  on  the  roof  would  be  sufficient  for  all  except  exposed  loca- 
tions. If  the  building  is  somewhat  protected  a  horizontal  pressure  of 
20  pounds  per  square  foot  on  the  sides  is  certainly  ample  for  heights 
less  than,  say,  30  feet. 

Wind  Pressure  on  Inclined  Surfaces. — The  wind  is  usually 
taken  as  acting  horizontally  and  the  normal  component  on  inclined  sur- 
faces is  calculated. 


14  WIND  LOADS 

The  normal  component  of  the  wind  pressure  on  inclined  surfaces 
has  usually  been  computed  by  Hutton's  empirical  formula 

Pn=Psin^    L842  cos  ^-1  (4) 

where  Pn  equals  the  normal  component  of  the  wind  pressure,  P  equals 
the  pressure  per  square  foot  on  a  vertical  surface,  and  A  equals  the 
angle  of  inclination  of  the  surface  with  the  horizontal,  Fig.  (5). 
The  formula  due  to  Duchemin 

P   ...  »     2sin^  (5) 

1  -f  sin2  A 

where  P  n,  P  and  A  are  the  same  as  in  (4),  gives  results  considerably 
larger  for  ordinary  roofs  than  Hutton's  formula,  and  is  coming  into 
quite  general  use. 
The  formula 

p         P  A  (6) 

Pn=  ~4SA 

where  P n  and  P  are  the  same  as  in  (4)  and  (5),  and  A  is  the  angle 
of  inclination  of  the  surface  in  degrees  (A  being  equal  to  or  less  than 
45°),  gives  results  which  agree  very  closely  with  Hutton's  formula, 
and  is  much  more  simple. 


FIG.  5. 

Hutton's  formula  (4)  is  based  on  experiments  which  were  very 
crude  and  probably  erroneous.  Duchemin's  formula  (5)  is  based  on 
very  careful  experiments  and  is  now  considered  the  most  reliable  form- 
ula in  use.  The  Straight  Line  formula  (6)  agrees  with  experiments 
quite  closely  and  is  preferred  by  many  engineers  on  account  of  its 
simplicity. 

The  values  of  P  n  as  determined  by  Hutton's,  Duchemin's  and  the 


NORMAL  WIND  PRESSURE  15 

Straight  Line  formulas  are  given  in  Fig.  6,  for  P  equals  20,  30  and 
40  pounds. 

It  is  interesting  to  note  that  Duchemin's  formula  with  P  equals  30 
pounds  gives  practically  the  same  values  for  roofs  of  ordinary  inclina- 
tion as  is  given  by  Button's  and  the  Straight  Line  formulas  with  P 
equals  40  pounds. 


Djchemn 

Mutton  

Straight  Line — 


Straight  Line  %=£A,(A  *45°) 


#»  Normal  Pnessune.lbs-per  sq  ft- 
/^Horizontal-          -    »       - 
A  =Angle  of  inclination  of  surface 


O    5    10    I  &   2O   25   30   35   40   45   50   55   60   65   TO   75   SO   65   9O 

Angle  Exposed  Roof  makes  with  Horizontal  in  Degrees  ,A. 

FIG.   6.    NORMAL   WIND   LOAD   ON   ROOF   ACCORDING   TO   DIFFERENT 

FORMULAS. 


Duchemin  has  also  deduced  the  formula 

_  •  2  sin2  A 


(7) 

where  P h    in   (7)   equals  the  pressure  parallel  to  the  direction  of  the 
wind,  Fig.  5;  and 

2  sin  A  cos  A  (8) 


P/  =  P 


1  -4-  sin2  A 


1 6  WIND  LOADS 

where  Ph  in  (8)  equals  the  pressure  at  right  angles  to  the  direction  of 
the  wind,  Fig.  5.  PI  may  be  an  uplifting,  a  depressing  or  a  side  pres- 
sure. With  an  open  shed  in  exposed  positions  the  uplifting  effect  of 
the  wind  often  requires  attention.  In  that  case  the  wind  should  be 
taken  normal  to  the  inner  surface  of  the  building  on  the  leeward  side, 
and  the  uplifting  force  determined  by  using  formula  (8).  If  the  gables 
are  closed  a  deep  cup  is  formed,  and  the  normal  pressure  should  be 
increased  30  to  70  per  cent. 

That  the  uplifting  force  of  the  wind  is  often  considerable  in  exposed 
localities  is  made  evident  by  the  fact  that  highway  bridges  are  occasion- 
ally wrecked  by  the  wind.  The  most  interesting  example  known  to  the 
author  is  that  of  a  loo-foot  span  combination  bridge  in  Northwestern 
Montana  which  was  picked  up  bodily  by  the  wind,  turned  about  90 
degrees  in  azimuth  and  dropped  into  the  middle  of  the  river.  The  end 
bolsters  were  torn  loose  although  drift-bolted  to  the  abutments.* 

The  wind  pressure  is  not  a  steady  pressure,  but  varies  in  intensity, 
thus  producing  excessive  vibrations  which  cause  the  structure  to  rock 
if  the  bracing  is  not  rigid.  The  bracing  in  mill  buildings  should  be 
designed  for  initial  tension,  so  that  the  building  will  be  rigid.  Rigidity 
is  of  more  importance  than  strength  in  mill  buildings. 

For  further  information  on  this  subject  see  a  very  elaborate  and 
valuable  monograph  on  "  Wind  Pressures  in  Engineering  Construc- 
tion," by  Capt.  W.  H.  Bixby,  M.  Am.  Soc.  C.  E.,  published  in  Engi- 
neering News,  Vol.  XXXIIL,  pp.  175-184,  March,  1895. 

Wind  Pressure  on  Office  Buildings. — The  following  specifica- 
tion for  wind  pressure  on  office  buildings  has  been  proposed  by  Mr. 
C.  C.  Schneider,  f 

Wind  Pressure. — The  wind  pressure  shall  be  assumed  at  30  Ib. 
per  sq.  ft.  acting  in  either  direction  horizontally : 

1.  On  the  sides  and  ends  of  buildings  and  on  the  actually  exposed 

surface,  or  the  vertical  projection  of  roofs; 

2.  On  the  total  exposed  surfaces  of  all  parts  composing  the  metal 

framework.     The  framework  shall  be  considered  an  inde- 
pendent structure,  without  walls,  partitions  or  floors. 

*  For  a  description  of  the  wreck  by  the  wind  of  the  High  Bridge  over 
the  Mississippi  River  at  St.  Paul,  Minn.,  see  article  by  C.  A.  P.  Turner  in 
Trans.  Am.  Soc.  C.  E.,  Vol.  54,  p.  31. 

f  Trans.  Am.   Soc.   C.  E.,  Vol.  54,   1905. 


CHAPTER  IV. 
MISCELLANEOUS  LOADS. 

LIVE  LOADS  ON  FLOORS.— Live  loads  on  floors  for  mill 
buildings  are  very  hard  to  classify  and  should  be  calculated  for  each 
case. 

Floor  loads  ar  specified  in  the  building  laws  of  various  cities  are 
g^ven  in  Table  II,  and  the  engineer  should  govern  himself  accordingly. 

TABLE  II. 

FLOOR  LOADS  IN  POUNDS  PER  SQUARE  FOOT  AS  SPECIFIED  IN  VARIOUS 

CITIES. 


New  York 

Chicago 

Philadelphia 

Boston 

Dwellings  

j  Upper  floors  75 

100 

100 

100 

Public  Buildings.  . 
Lig-ht  Manufac- 
turing" 

}  1st  floor        ,50 
90 

19Q 

100 

100 

120 
100 

150 

Warehouses  and 
Factories    

150  and  up 

150  and  up 

250  and  up 

Sidewalks  

300 

Without  reference  to  building  laws  the  live  loads  per  square  foot, 
exclusive  of  weight  of  floor  materials,  given  below  are  about  standard 
practice. 

Dwellings    70  Ibs.  per  sq.  ft. 

Offices    70  to  ico  Ibs.  per  sq.  ft. 

Assembly  halls   120  to  1 50  Ibs.  per  sq.  ft. 

Warehouses    250  and  up,  Ibs.  per  sq.  ft. 

Factories    200  to  450  Ibs.  per  sq.  ft. 


i8 


MISCELLANEOUS  LOADS 


The  weight  of  floors  above  ground  in  mill  buildings  varies  so 
much  that  it  is  useless  to  give  weights.  For  a  few  data  on  weights 
of  floors  see  Chapter  on  Floors. 

WEIGHT  OF  HAND  CRANES.— The  approximate  weight  of 
a  few  of  the  common  sizes  of  hand  cranes  made  by  Pawling  and  Har- 

TABLE  III. 
WEIGHT  OF  TRAVELING  HAND  CRANES. 


Capacity  of 
Crane  in 
Tons 

Distance 
c  to  c  of 
end  wheels 

20-FOOT  SPAN 

30-FOOT  SPAN 

Weight  of 
Crane 
Ibs. 

Maximum  Load 
on  each  Wheel 
Ibs. 

Weight  of 
Crane 
Ibs. 

Maximum  Load 
on  each  Wheel 
Ibs. 

3 
5 
7^ 
10 
15 
20 

3'  —  0" 
3'  —  0" 

3'—  8" 
8'  —  0" 
8'  —  0" 
8'  —  6" 

4500 

5500 
8000 
15000 
16000 
20000 

4500 

7000 
10500 
18000 
20000 
26000 

5000 
6000 
9000 
17000 
18000 
22000 

5000 
7500 
11500 
20000 
21000 
27000 

nischfeger,  Milwaukee,  Wis.,  and  the  maximum  load  on  each  wheel 
when  the  loaded  trolley  is  at  one  end  is  given  in  Table  III. 


40  50  60  70 

Span  of  Crane  in  Feet 

FIG.  7. 

WEIGHT  OF  ELECTRIC  CRANES.— The  maximum  load  on 
each  of  the  end  wheels  for  common  sizes  of  electric  cranes  made  by 


WEIGHT  OF  ELECTRIC  CRANES 


19 


Pawling  and  Harnischfeger  is  given  in  Fig.  7.  Cranes  made  by  different 
manufacturers  differ  considerably  in  weight. 

The  weights  and  dimensions  of  typical  traveling  cranes  as  given 
in  Table  Ilia  have  been  proposed  for  adoption  as  a  standard. 

TABLE  Ilia. 
TYPICAL  ELECTRIC  TRAVELING  CRANES.* 


Capacity  in 
Tons.     . 

Span. 

Wheel  Base. 

Maximum 
Wheel  Load, 
in  Pounds. 

«. 

V. 

Weight  of  Rail  for  : 

Plate  Girders. 

Beams. 

5 

40 
60 
40 
60 
40 
60 
40 
60 
40 
60 
40 
60 
40 
60 
40 
60 

8  ft.  6  in. 
9       0 
9       0 
9       6 
9       6 
10       0 
10       0 
10       6 
10       0 
10       6 
10       6 
11       0 
11       0 
12       0 
11       0 
12       0 

12,000 
13,000 
19,000 
21,000 
26,000 
29,000 
33,000 
36,000 
40,000 
44,000 
48,000 
52,000 
64,000 
70,000 
72,000 
80,000 

10  in. 

t 

t 

< 

< 

< 

12  in. 
« 
« 
« 
« 
« 

Win. 
« 
« 
« 

7  ft. 
« 
« 

u 
It 

« 

8  ft. 

< 

< 
i 

9  ft. 
« 

40  Ib.  per  yd. 
40        " 
45 
45 
50 
50 
55 
55 
60 
60 
70 
70 
80 
80 
100 
100 

40 
40 
40 
40 
50 
50 
50 
50 
50 
50 
60 
60 
60 
60 
60 
60 

10 

15  

20 

25     ...      . 

30  

40  

50  

1.  Wheel-load  can  be  assumed  as  distributed  in  top  flange,  over  a 
distance  equal  to  depth  of  girder,  with  a  maximum  limit  of  30  in. 

2.  In  addition  to  the  vertical  load,  the  top  flanges  of  the  girder 
shall  withstand  a  lateral  loading  of  two-tenths  of  the  lifting  capacity 
of  the  crane,  equally  divided  between  the  four  wheels  of  the  crane. 

s  =  Side  clearance  from  center  of  rail. 
v  =  Vertical  clearance  from  top  of  rail. 

3.  The  top  flanges  of  the  crane  girders  shall  not  be  of  smaller 
width  than  one-twentieth  of  their  unsupported  length. 

WEIGHTS    OF    MISCELLANEOUS    MATERIAL.— The 

weights  of  various  kinds  of  merchandise  are  given  in  Table  IV.     For 
weights  of  other  materials  consult  steel  makers  hand  books. 

*Mr.  C.  C.  Schneider  in  Trans.  Am.  Soc.  C.  E.,  Vol.  54,  1905.    Also  see 
Tables  25  and  26,  Appendix  III. 


20 


MISCELLANEOUS  LOADS 

TABLE  IV. 
WEIGHTS  OF  MERCHANDISE.* 


Commodity 

Weight  in  Ibs. 
per  cubic  foot 

Commodity 

Weight  in  Ibs. 
per  cubic  foot 

Wool  in   Bales 

5  to  28 

88 

Woolen  Goods  .... 

13  to  22 

Barrel  Starch  

23 

Baled  Cotton  

12  to  43 

Barrel  Lime  

50 

Cotton  Goods  

11  to  37 

"       Cement  

73 

Rag's  in  Bales... 

7  to  36 

'•       Plaster     .... 

53 

Paper  

10  to  69 

Lard  Oil  

34 

Wheat      

39  to  44 

Rope  

42 

Corn  

31 

Box  Tin  

278 

Oats   

27 

60 

Baled  Hay  and  Straw. 

14  to  19 

Crate  Crockery  

40 

Bleaching*   Powder 

31 

Bale  Leather  

16  to  23 

Soda  Ash    

62 

Sujrar  • 

45 

Box  Indigo           

43 

Cheese  

30 

The   weights   of   miscellaneous   building   materials   are   given   in 
Table  IVa. 

TABLE  IVa. 

WEIGHTS  OF  BUILDING  MATERIALS. 


Material. 

Weight  Ibs.  per 
cu,  ft. 

Material. 

Weight  Ibs.  per 
cu.  ft. 

Paving  brick 

150 

Glass 

160 

Common  building  brick 

120 

Snow,  freshly  fallen  

10 

Soft  building  brick  

100 

Snow,  wet       

50 

Granite  

170 

Spruce   

25 

Marble  

170 

Hemlock   

25 

160 

White  pine  

25 

Sandstone                   

145 

Douglas  fir                  .. 

30 

Slag... 

40 

Yellow  pine  

40 

Gravel   

120 

White  oak     

50 

Slate  

175 

Common  brickwork  

100-120 

Sand,  clay  and  earth  (dry) 

100 

Rubble  masonry 

130-150 

Sand,  clay  and  earth  (wet). 

120 

Ashlar  masonry 

140-160 

Mortar   

100 

Cast  iron 

450 

Stone  concrete  

130-150 

Wrought  iron  

480 

Cinder  concrete  

70 

Steel  

490 

Paving  asphaltum  

100 

Plaster,  ceiling  

10  to  15  Ib. 

Plaster  of  paris  

140 

per  sq    ft. 

*  From  Report  V.     Insurance  Engineering  Experiment  Station. 
Atkinson,  Director,  Boston,  Mass. 


Edward 


LIVE  LOADS 


21 


CONCENTRATED  LIVE  LOADS.— The  loads  given  in  Table 
Ha  have  been  proposed  for  different  classes  of  buildings.*  These 
loads  consist  of : 

(a)  A  uniform  load  per  square  foot  of  floor  area; 

(b)  A  concentrated  load  which  shall  be  applied  to  all  points 

of  the  floor ; 

(c)  A  uniform  load  per  linear  foot  for  girders. 
The  maximum  result  is  to  be  used  in  calculations. 

The  specified  concentrated  loads  shall  also  apply  to  the  floor  con- 
struction between  the  beams  for  a  length  of  five  feet. 

TABLE  Ha. 

LlVE  LOADS  FOR  FLOORS. 


Classes  of  Buildings. 

Live  Loads,  in  Pounds. 

Distributed 
Load. 

Concentrated 
Load. 

Load  per  Li  near 
Foot  of  Girder. 

Dwellings,    hotels,    apartment-houses,    dormi- 
tories  hospitals 

40 
50 
60 

80 

)     floor  100 
|  columns  SO 

80 
300 
from  120  up 
"    300  " 

r 

"    200  "  \ 

[ 

2,000 
5,000 
5,000 

5,000 
|   5,000 

8,000 
10,000 
Special. 
it 

The  actuj 
gines,  boile 
shall  be  use 
less  than  20 

500 
1,000 
1,000 

1,000 
1,000 

1,000 
1,000 
Special. 
tt 

il  weights  of  en- 
rs,   stacks,   etc., 
rl,  but  in  no  case 
Olb.  per  sq.  ft... 

Office  buildings,  upper  stories                   ... 

Schoolrooms,  theater  galleries,  churches  

Ground  floors  of  office  buildings,  corridors  and 
stairs  in  public  buildings  

Assembly  rooms,  main  floors  of  theaters,  ball- 
rooms, gymnasia,  or  any  room  likely  to  be 
used  for  drilling  or  dancing 

Ordinary  stores  and  light  manufacturing,  stables 
and  carriage-houses     

Warehouses  and  factories  

Charging  floors  for  foundries 

Power-houses,  for  uncovered  floors  

If  heavy  concentrations,  like  safes,  armatures,  or  special  machinery, 
are  likely  to  occur  on  floors,  provision  should  be  made  for  them. 


*  Mr.  C.  C.  Schneider  in  Trans.  Am.  Soc.  C  E.,  Vol.  54,  1905. 


PART   II. 

STRESSES. 

CHAPTER  V. 
GRAPHIC  STATICS. 

Equilibrium. — Statics  considers  forces  as  at  rest  and  therefore  in 
equilibrium.  To  have  static  equilibrium  in  any  system  of  forces  there 
must  be  neither  translation  nor  rotation  and  the  following  conditions 
must  be  fulfilled  for  coplanar  forces  (forces  in  one  plane). 

S  horizontal    components    of    forces    =  o  (a) 

3  vertical    components    of    forces         =  o  (b) 

S  moments  of  forces  about  any  point  =  o  (c) 

Representation  of  Forces. — A  force  is  determined  when  its 
magnitude,  line  of  action,  and  direction  are  known,  and  it  may  be  rep- 
resented graphically  in  magnitude  by  the  length  of  a  line,  in  line  of 
action  by  the  position  of  the  line,  and  in  direction  by  an  arrow  placed 
on  the  line,  pointing  in  the  direction  in  which  the  force  acts.  A  force 
may  be  considered  as  applied  at  any  point  in  its  line  of  action. 

Force  Triangle.— The  resultant,  R,  of  the  two  forces  P±  and  P2 
meeting  at  the  point  a  in  Fig.  8  is  represented  in  magnitude  and  direc- 
tion by  the  diagonal,  R,  of  the  parallelogram  abed.  The  combining 
of  the  two  forces  Pt  and  P2  into  the  force  R  is  termed  composition  of 
forces.  The  reverse  process  is  called  resolution  of  forces. 


FORCE  TRIANGLE  23 

Pa 


(c) 


The  value  of  R  may  also  be  found  from  the  equation 
R2  =  P^  +  P22  +  2  PI  P2  cos  0 

It  is  not  necessary  to  construct  the  entire  force  parallelogram  as 
in  (a)  Fig.  8,  the  force  triangle  (b)  below  or  (c)  above  the  resultant  R 
being  sufficient. 

If  only  one  force  together  with  the  line  of  action  of  the  two  others 
be  given  in  a  system  containing  three  forces  in  equilibrium,  the  magni- 
tude and  direction  of  the  two  forces  may  be  found  by  means  of  the 
force  triangle. 

If  the  resultant  R  in  Fig.  8  is  replaced  by  a  force  £  equal  in 
amount  but  opposite  in  direction,  the  system  of  forces  will  be  in  equi- 
librium, (a)  or  (b)  Fig.  9.  The  force  H  is  the  equilibrant  of  the  system 
of  forces  P±  and  P2. 


It  is  immaterial  in  what  order  the  forces  are  taken  in  constructing 
the  force  triangle,  as  in  Fig.  9,  as  long  as  the  forces  all  act  in  the  same 
direction  around  the  triangle.  The  force  triangle  is  the  foundation 
of  the  science  of  graphic  statics. 


24  GRAPHIC  STATICS 

Force  Polygon. — If  more  than  three  concurrent  forces  (forces 
which  meet  in  a  point)  are  in  equilibrium  as  in  (a)  Fig.  10,  R^  in  (b) 
will  be  the  resultant  of  Px  and  P2,  R2  will  be  the  resultant  of  R^  and  P3, 


FIG.  10. 


and  will  also  be  the  equilibrant  of  P4  and  P5.  The  force  polygon  in  (b) 
is  therefore  only  a  combination  of  force  triangles.  The  force  polygon 
for  any  system  of  forces  may  be  constructed  as  follows  :  —  Beginning 
at  any  point  draw  in  succession  lines  representing  in  magnitude  and 
direction  the  given  forces,  each  line  beginning  where  the  preceding  one 
ends.  If  the  polygon  closes  the  system  of  forces  is  in  equilibrium,  if 
not  the  line  joining  the  first  and  last  points  represents  the  resultant 
in  magnitude  and  direction.  As  in  the  case  of  the  force  triangle,  it 
is  immaterial  in  what  order  the  forces  are  applied  as  long  as  they 
all  act  in  the  same  direction  around  the  polygon.  A  •  force  polygon  is 
analogous  to  a  traverse  of  a  field  in  which  the  bearings  and  the  distances 
are  measured  progressively  around  the  field  in  either  direction.  The 
conditions  for  closure  in  the  two  cases  are  also  identical. 

It  will  be  seen  that  any  side  in  the  force  polygon  is  the  equilibrant 
of  all  the  other  sides  and  that  any  side  reversed  in  direction  is  the  re- 
sultant of  all  the  other  sides. 

Equilibrium  of  Concurrent  Forces.  —  The  necessary  condition 
for  equilbrium  of  concurrent  coplanar  forces  therefore  is  that  the  force 
polygon  close.  This  is  equivalent  to  the  algebraic  condition  that  2 
horizontal  components  of  forces  ==  o,  and  S  vertical  components  of 
forces  =  o.  If  the  system  of  concurrent  forces  is  not  in  equilibrium 
the  resultant  can  be  found  in  magnitude  and  direction  by  completing 


EQUILIBRIUM  OF  FORCES 


25 


the  force  polygon.     The  resultant  of  a  system  of  concurrent  forces 
is  always  a  single  force  acting  through  their  point  of  intersection. 

Equilibrium  of  Non-concurrent  Forces. — If  the  forces  are 
non-concurrent  (do  not  all  meet  in  a  common  point),  the  condition  that 
the  force  polygon  close  is  a  necessary,  but  not  a  sufficient  condition  for 
equilibrium.  For  example,  take  the  three  equal  forces  Plf  P2  and  P3, 
making  an  angle  of  120°  with  each  other  as  in  (a)  Fig.  n. 


Resultant  Moment 
=  -F?h 


(a) 


Positive  Moment 
Moment=+Ph 


FIG.  ii 


Negative  Moment 
Moment  =  -Ph 

(c) 


The  force  polygon  (b)  closes,  but  the  system  is  not  in  equilibrium. 
The  resultant,  R,  of  P2  and  P3  acts  through  their  intersection  and  is 
parallel  to  Plt  but  is  opposite  in  direction.  The  system  of  forces  is  in 
equilibrium  for  translation,  but  is  not  in  equilibrium  for  rotation. 

The  resultant  of  this  system  is  a  couple  with  a  moment  =  —  P±  h, 
moments  clockwise  being  considered  negative  and  counter  clockwise 
positive,  (c)  Fig.  n.  The  equilibrant  of  the  system  in  (a)  Fig.  n  is 
a  couple  with  a  moment  =  -j-  P1  h. 

A  couple. — A  couple  consists  of  two  parallel  forces  equal  in 
amount,  but  opposite  in  direction.  The  arm  of  the  couple  is  the  per- 
pendicular distance  between  the  forces.  The  moment  of  a  couple  is 
equal  to  one  of  the  forces  multiplied  by  the  arm.  The  moment  of  a 
couple  is  constant  about  any  point  in  the  plane  and  may  be  represented 


26  GRAPHIC  STATICS 

graphically  by  twice  the  area  of  the  triangle  having  one  of  the  forces 
as  a  base  and  the  arm  of  the  couple  as  an  altitude.  The  moment  of  a 
force  about  any  point  may  be  represented  graphically  by  twice  the 
area  of  a  triangle  as  shown  in  (c)  Fig.  n. 

It  will  be  seen  from  the  preceding  discussion  that  in  order  that  a 
system  of  non-concurrent  forces  be  in  equilibrium  it  is  necessary  that  the 
resultant  of  all  the  forces  save  one  shall  coincide  with  the  one  and  be 
opposite  in  direction.  Three  non-concurrent  forces  can  not  be  in  equi- 
librium unless  they  are  parallel.  The  resultant  of  a  system  of  non- 
concurrent  forces  may  be  a  single  force  or  a  couple. 

Equilibrium  Polygon. — First  Method. — In  Fig.  12  the  resultant, 
a,  of  P!  and  P2  acts  through  their  intersection  and  is  equal  and  parallel 
to  a  in  the  force  polygon  (a)  ;  the  resultant,  b,  of  a  and  P3  acts  through 


FIG.  12. 


their  intersection  and  is  equal  and  parallel  to  b  in  the  force  polygon ; 
the  resultant,  c,  of  b  and  P4  acts  through  their  intersection  and  is  equal 
and  parallel  to  c  in  the  force  polygon ;  and  finally  the  resultant,  R,  of  c 
and  P5  acts  through  their  intersection  and  is  equal  and  parallel  to  R 
in  the  force  polygon.  R  is  therefore  the  resultant  of  the  entire  system 
of  forces.  If  R  is  replaced  by  an  equal  and  opposite  force,  £,  the  sys- 
tem of  forces  will  be  in  equilibrium.  Polygon  (a)  in  Fig.  12  is  called 


EQUILIBRIUM  POLYGON  27 

a  force  polygon  and  (b)  is  called  a  funicular  6r  an  equilibrium  polygon. 
It  will  be  seen  that  the  magnitude  and  direction  of  the  resultant  of  a 
system  of  forces  is  given  by  the  closing  line  of  the  force  polygon,  and 
the  line  of  action  is  given  by  the  equilibrium  polygon. 

The  force  polygon  in  (a)  Fig.  13  closes  and  the  resultant,  R,  of 


Resultant  Moment 

=  -P6h 

FIG.  13. 

the  forces  Plf  P2,  Pz,  P±,  P5  is  parallel  and  equal  to  P6,  and  is  opposite 
in  direction.  The  system  is  in  equilibrium  for  translation,  but  is  not  in 
equilibrium  for  rotation.  The  resultant  is  a  couple  with  a  moment 
=  —  P6  h.  The  equilibrant  of  the  system  of  forces  will  be  a  couple 
with  a  moment  =  4-^0  '*•  From  the  preceding  discussion  it  will  be 
seen  that  if  the  force  polygon  for  any  system  of  non-concurrent  forces 
closes  the  resultant  will  be  a  couple.  If  there  is  perfect  equilibrium 
the  arm  of  the  couple  will  be  zero. 

Second  Method. — \Yhere  the  forces  do  not  intersect  within  the 
limits  of  the  drawing  board,  or  where  the  forces  are  parallel,  it  is  not 
possible  to  draw  the  equilibrium  polygon  as  shown  in  Fig.  12  and  Fig. 
13,  and  the  following  method  is  used. 

The  point  o,  (a)  Fig.  14,  which  is  called  the  pole  of  the  force  poly- 
gon, is  selected  so  that  the  strings  a  o,  b  o,  c  o,  d  o  and  e  o  in  the  equi- 
librium polygon  (b),  which  are  drawn  parallel  to  the  corresponding 


28  GRAPHIC  STATICS 

rays  in  the  force  polygon  (a),  will  make  good  intersections  with  the 
forces  which  they  replace  or  equilibrate. 

In  the  force  polygon  (a),  P±  is  equilibrated  by  the  imaginary  forces 
represented  by  the  rays  o  a  and  b  o  acting  as  indicated  by  the  arrows 
within  the  triangle;  P2  is  equilibrated  by  the  imaginary  forces  repre- 


FIG.  14. 


sented  by  the  rays  o  b  and  c  o  acting  as  indicated  by  the  arrows  within 
the  triangle  ;  P3  is  equilibrated  by  the  imaginary  forces  represented  by 
the  rays  o  c  and  d  o  acting  as  indicated  by  the  arrows  within  the  tri- 
angle ;  and  P4  is  equilibrated  by  the  imaginary  forces  o  d  and  e  o  acting 
as  indicated  by  the  arrows  within  the  triangle.  The  imaginary  forces 
are  all  neutralized  except  a  o  and  o  e,  which  are  seen  to  be  components 
of  the  resultant  R. 

To  construct  the  equilibrium  polygon,  take  any  point  on  the  line 
of  action  of  P1  and  draw  strings  o  a  and  o  b  parallel  to  rays  o  a  and  o  b, 
Z?  o  is  the  equilibrant  of  o  a  and  P1;  through  the  intersection  of  string 
o  b  and  P2  draw  string  c  o  parallel  to  ray  c  o,  c  o  is  the  equilibrant  of 
o  b  and  P2  ;  through  the  intersection  of  string  c  o  and  P3  draw  string 
d  o  parallel  to  ray  d  o,  d  o  is  the  equilibrant  of  c  o  and  P3  ;  and  through 
the  intersection  of  string  d  o  and  P4  draw  string  e  o  parallel  io  ray  e  o, 
e  o  is  the  equilibrant  of  d  o  and  P4.  Strings  o  a  and  e  o  acting  as  shown 
are  components  of  the  resultant  R,  which  will  be  parallel  to  R  in  the 
force  polygon  and  acts  through  the  intersections  of  strings  o  a  and  e  o. 


REACTIONS  OF  A  BEAM 


29 


The  imaginary  forces  represented  by  the  rays  in  the  force  poly- 
gon may  be  considered  as  components  of  the  forces  and  the  analysis 
made  on  that  assumption  with  equal  ease. 

It  is  immaterial  in  what  order  the  forces  are  taken  in  drawing 
the  force  polygon,  as  long  as  the  forces  all  act  in  the  same  direction 
around  the  force  polygon,  and  the  strings  meeting  on  the  lines  of  the 
forces  in  the  equilibrium  polygon  are  parallel  to  the  rays  drawn  to  the 
ends  of  the  same  forces  in  the  force  polygon. 

The  imaginary  forces  a  o,b  o,  c  o,  d  o,  e  o  are  represented  in  mag- 
nitude and  in  direction  by  the  rays  of  the  force  polygon  to  the  same 
scale  as  the  forces  P±,  P2,  P3,  P±.  The  strings  of  the  equilibrium  poly- 
gon represent  the  imaginary  forces  in  line  of  action  and  direction,  but 
not  in  magnitude. 

Reactions  of  a  Simple  Beam. — The  equilibrium  polygon  may 
be  used  to  obtain  the  reactions  of  a  beam  loaded  with  a  load  P  as  in 
Fig.  15. 


S-r-^O 


(a) 


FIG.  15. 


The  force  polygon  (b)  is  drawn  with  a  pole  o  at  any  convenient 
point  and  rays  o  a  and  o  c  are  drawn.  Now  from  the  fundamental  con- 
ditions for  equilibrium  for  translation  we  have  P  =  Rt  -{-  R2.  At  any 
convenient  point  in  the  line  of  action  of  P  draw  the  strings  o  a  and  o  c 
parallel  to  the  rays  o  a  and  o  c,  respectively,  in  the  force  polygon.  The 
imaginary  forces  a  o  and  o  c  acting  as  shown  equilibrate  the  force  P. 


3° 


GRAPHIC  STATICS 


The  imaginary  force  a  o  acting  in  a  reverse  direction  as  shown 
is  an  equilibrant  of  R1}  and  the  imaginary  force  c  o  acting  in  a  reverse 
direction  is  an  equilibrant  of  R2.  The  remaining  equili brant  of  R-L  and 
of  R2  must  coincide  and  be  equal  in  amount,  but  opposite  in  direction. 
The  string  &  o  is  the  remaining  equilibrant  of  7^  and  of  R2  and  is 
called  the  closing  line  of  the  equilibrium  polygon.  The  ray  b  o  drawn 
parallel  to  the  string  b  o  divides  P  in  two  parts  which  are  equal  to  the 
reactions  R^  and  R2  (for  reactions  of  overhanging  beam  see  Chapter 
VIII). 

Reactions  of  a  Cantilever  Truss. — In  the  cantilever  truss  shown 
in  Fig.  1 6,  the  direction  and  point  of  application  B  of  the  reaction  R^ 


FIG.  16. 

are  known,  while  the  point  of  application  A  of  the  reaction  R2  only 
is  known.  The  direction  of  reaction  R2  may  be  found  by  applying  the 
principle  that  if  a  body  is  in  equilibrium  under  the  action  of  three 
external  forces  which  are  not  parallel,  they  must  all  meet  in  a  common 
point,  i.  e.,  the  forces  must  be  concurrent.  The  resultant  of  all  the 
loads  acts  through  the  point  c,  which  is  also  the  point  of  intersection 
of  the  reactions  R±  and  R2.  Having  the  direction  of  the  reaction  R2) 
the  values  of  the  reactions  may  be  found  by  means  of  a  force  polygon. 
The  direction  of  reaction  R2  may  be  found  by  means  of  a  force  and 
equilibrium  polygon  as  follows :  Construct  the  force  polygon  (b)  with 
pole  o  and  draw  equilibrium  polygon  (a)  starting  with  point  A,  the 


EQUILIBRIUM  POLYGON  AS  A  FRAMED  STRUCTURE 


31 


only  known  point  on  the  reaction  R2,  and  draw  the  polygon  as  prev- 
iously described.  A  line  drawn  through  point  o  in  the  force  polygon 
parallel  to  the  closing  line  of  the  equilibrium  polygon  will  meet  Rlt 
drawn  parallel  to  reaction  Rlt  in  the  point  y,  which  is  also  a  point  on  R.2. 
The  reactions  R^  and  R»  are  therefore  completely  determined  in  direc- 
tion and  amount. 

The  method  just  given  is  the  one  commonly  used  for  finding  the  re- 
actions in  a  truss  with  one  end  on  rollers  (see  Chapter  VII). 

Equilibrium  Polygon  as  a  Framed  Structure. — In  (a)  Fig. 
17,  the  rigid  triangle  supports  the  load  Pi.  Construct  a  force  polygon 


R, 


(a) 


FIG.  17. 


by  drawing  rays  a  i  and  c  I  in  (b)  parallel  to  sides  a  I  and  c  I,  respec- 
tively, in  (a),  and  through  pole  I  draw  I  b  parallel  to  side  I  b  in  (a). 
The  reactions  R±  and  R2  will  be  given  by  the  force  polygon  (b),  and 
the  rays  i  a,  i  c  and  I  b  represent  the  stresses  in  the  members  I  a,  i  c 
and  i  b,  respectively,  in  the  triangular  structure.  The  stresses  in  I  a 
and  i  c  are  compression  and  the  stress  in  i  b  is  tension,  forces  acting 
toward  the  joint  indicating  compression  and  forces  acting  away  from 
the  joint  indicating  tension.  Triangle  (a)  is  therefore  an  equilibrium 
polygon  and  polygon  (b)  is  a  force  polygon  for  the  force  Px. 

From  the  preceding  discussion  it  will  be  seen  that  the  internal 
stresses  at  any  point  or  in  any  section  hold  in  equilibrium  the  external 
forces  meeting  at  a  point  or  on  either  side  of  the  section. 


32 


GRAPHIC  STATICS 


Graphic  Moments.  —  In  Fig.  18  (b)  is  a  force  polygon  and  (a) 
is  an  equilibrium  polygon  for  the  system  of  forces  Plf  Pz,  Pz,  P±.    Draw 


bS^^L 


FIG.  18. 

the  line  M  N  =  Y  parallel  to  the  resultant  R,  and  with  ends  on  strings 
o  e  and  o  a  produced.  Let  r  equal  the  altitude  of  the  triangle  L  M  N 
and  H  equal  the  altitude  of  the  similar  triangle  o  e  a.  H  is  the  pole 
distance  of  the  resultant  R. 

Now  in  the  similar  triangles  L  M  N  and  o  e  a 

R  :Y  :  :H  :r 
and  R  r  =  H  Y 

But  R  r  =  M  =  moment  of  resultant  R  about  any  point  in  the  line 
M  N  and  therefore 

M  =  H  Y 

The  statement  of  the  principle  just  demonstrated  is  as  follows: 
The  moment  of  any  system  of  coplanar  forces  about  any  point  in 
the  plane  is  equal  to  the  intercept  on  a  line  drawn  through  the  center 
of  moments  and  pa'rallel  to  the  resultant  of  all  the  forces,  cut  off  by  the 
strings  which  meet  on  the  resultant,  multiplied  by  the  pole  distance  of 
the  resultant.  It  should  be  noted  that  in  all  cases  the  intercept  is  a 
distance  and  the  pole  distance  is  a  force. 

This  property  of  the  equilibrium  polygon  is  frequently  used  in 
finding  the  bending  moment  in  beams  and  trusses  which  are  loaded  with 
vertical  loads. 


BENDING  MOMENTS  IN  A  BEAM 


33 


Bending  Moments  in  a  Beam. — It  is  required  to  find  the  mo- 
ment at  the  point  M  in  the  simple  beam  loaded  as  in  (b)  Fig.  19.    The 


at1 


(a) 


FIG.  19. 


moment  at  M  will  be  the  algebraic  sum  of  the  moments  of  the  forces 
to  the  left  of  M.  The  moment  of  P±  =  H  x  B  C,  the  moment  of  P2  = 
H  x  C  D  and  the  moment  oi£i=  —  H  x  B  A.  The  moment  at  M  will 
therefore  be 


The  moment  of  the  forces  to  the  right  of  M  may  in  like  manner  be 
shown  to  be 


In  like  manner  the  bending  moment  at  any  point  in  the  beam  may  be 
shown  to  be  the  ordinate  of  the  equilibrium  polygon  multiplied  by  the 
pole  distance.  The  ordinate  is  a  distance  and  is  measured  by  the  same 
scale  as  the  beam,  while  the  pole  distance  is  a  force  and  is  measured 
by  the  same  scale  as  the  loads. 

To  Draw  an  Equilibrium  Polygon  Through  Three  Points.  — 
Given  a  beam  loaded  as  shown  in  Fig.  20,  it  is  required  to  draw 
an  equilibrium  polygon  through  the  three  points  a,  b,  c.  Construct  a 
force  polygon  (b)  with  pole  o,  and  draw  equilibrium  polygon  a  b'  c'  in 
(a).  Point  b'  is  determined  by  drawing  through  b  a  line  b  b'  parallel 
to  &x  b"  which  is  the  line  of  action  of  the  resultants  of  the  forces  to  the 


34 


GRAPHIC  STATICS 


(b) 


FIG.  20. 


left  of  b,  acting  through  points  b  and  a.  Through  o  draw  o  c"  and 
o  b"  parallel  to  closing  lines  a  c'  and  a  b',  respectively.  Point  c"  de- 
termines the  reactions  R^  and  R2,  and  point  b"  determines  the  reac- 
tions acting  through  a  and  b  of  the  forces  to  the  left  of  point  b. 

Points  c"  and  b"  are  common  to  all  force  polygons,  and  lines 
c"  o'  and  b"  o'  drawn  parallel  to  the  closing  lines  of  the  required  equi- 
librium polygon,  a  c  and  a  b  will  meet  in  the  new  pole  o'.  With  pole  o9 
the  required  equilibrium  polygon  a  b  c  can  now  be  drawn. 

Center  of  Gravity. — To  find  the  center  of  gravity  of  the  figure 
shown  in  (a)  Fig.  21,  proceed  as  follows:  Divide  the  figure  into 
elementary  figures  whose  centers  of  gravity  and  areas  are  known. 
Assume  that  the  areas  act  as  the  forces  Plt  P2f  P3  through  the  centers 
of  gravity  of  the  respective  figures.  Bring  the  line  of  action  of  these 
forces  into  the  plane  of  the  paper  by  turning  them  downward  as  in 
(b)  and  to  the  right  as  in  (c).  Find  the  resultant  of  the  forces  for 
case  (b)  and  for  case  (c)  by  means  of  force  and  equilibrium  polygons. 
The  intersection  of  the  resultants  R  will  be  the  center  of  gravity  of  the 
figure.  The  two  sets  of  forces  may  be  assumed  to  act  at  any  angle, 
however,  maximum  accuracy  is  given  when  the  forces  are  assumed  to 
act  at  right  angles.  If  the  figure  has  an  axis  of  symmetry  but  one 
force  and  equilibrium  polygon  is  required. 


MOMENT  OF  INERTIA  OF  FORCES 


35 


b) 


FIG.  21. 


Moment  of  Inertia  of  Forces. — The  determination  of  the  moment 
of  inertia  of  forces  and  areas  fry  graphics  is  interesting.  There 
are  two  methods  in  common  use:  (i)  Culmann's  method,  in  which 
the  moment  of  inertia  of  forces  is  determined  by  finding  the  moment 
of  the  moment  of  forces  by  means  of  force  and  equilibrium  polygons  > 
and  (2)  Mohr's  method,  in  which  the  moment  of  inertia  of  forces  is 
determined  from  the  area  of  the  equilibrium  polygon.  The  moment  of 
inertia  of  a  force  about  a  parallel  axis  is  equal  to  the  force  multiplied  by 
the  square  of  the  distance  between  the  force  and  the  axis. 

Culmann's  Method. — It  is  required  to  find  the  moment  of  inertia, 
/,  of  the  system  of  forces  Plt  P2)  P3,  P4,  Fig.  22,  about  the  axis  M  N. 
Construct  the  force  polygon  (a)  with  a  pole  distance  H,  draw 
the  equilibrium  polygon  abode,  and  produce  the  strings  until  they 
intersect  the  axis  M  N.  Now  the  moment  of  P±  about  axis  M  N  equals 
£  D  x  H;  moment  of  P2  equals  D  C  x  H;  moment  of  P3  equals  C  B  x 
H;  moment  of  P4  equals  B  A  x  H;  and  moment  of  resultant  R  equals 
£  A  x  H.  With  intercepts  £  D,  D  C,  C  B,  B  A,  as  forces  acting  in  place 
of  Plt  P2,  P3f  Pi,  respectively,  construct  force  polygon  (b)  with  pole 
distance  H',  and  draw  equilibrium  polygon  (c).  'As  before  the  moments 
of  the  forces  will  be  equal  to  the  products  of  the  intercepts  and  pole 
distance  and  the  moment  of  the  system  of  forces  represented  by  the 


GRAPHIC  STATICS 


K 

tel 

A 

£4 

g^^_H'  ^ 

Culmanris  Method 

^  j 

•  1  — 
i 

-^a-^^ 

,    I  of  Forces  a  bout 

•                 K    /I        N     1 

ID                      ^-'" 

axis  M-N 

^,»*                              r 

tQ            _   r—r-^  X  I—  1  X  1   |* 

^ 

F      ^^"                       P 

^x^ 

v 

f-T'      (b)         ', 

^          .^^^ 

< 

R 

"***"*"—-      ^         yv 

\ 

^""'^  \ 

R 

cT  x-x^ 

^ 

•6      • 

^^ 

(a) 


FIG. 


intercepts  will  be  equal  to  the  intercept  G  F  multiplied  by  pole  distance 
H'.  But  the  intercepts  £  D,  D  C,  C  B,  B  A,  multiplied  by  the  pole 
distance  H  equal  moments  of  the  forces  Plt  P2,  Pz,  P4,  respectively, 
about  the  axis  M  N,  and  the  moment  of  inertia  of  the  system  of  forces 
P!,  P2t  P3,  P4,  about  the  axis  M  N  will  be  equal  to  the  intercept  G  F 
multiplied  by  the  product  of  the  two  pole  distances  H  and  H',  and 

I  =  F  GxHxH' 

Mohr's  Method. — It  is  required  to  find  the  moment  of  inertia, 
/,  of  the  system  of  forces  Plt  P2,  P3,  P±,  Fig.  23,  about  the  axis  M  N. 
Construct  the  force  polygon  (a)  with  a  pole  distance  H,  and  draw  the 
equilibrium  polygon  (b) .  Now  the  moment  of  Px  about  the  axis  M  N 
equals  intercept  F  G  multiplied  by  the  pole  distance  H,  and  the  moment 
of  inertia  of  Pj  about  the  axis  M  N  equals  the  moment  of  the  moment  of 
P±  about  the  axis,  —  F  G  x  H  x  d.  But  F  G  x  d  equals  twice  the  area 
of  the  triangle  F  G  A,  and  we  have  the  moment  of  inertia  of  Px  equal  to 
the  area  of  the  triangle  F  G  A  x  2  H.  In  like  manner  the  moment  of 
inertia  of  P2  may  be  shown  equal  to  area  of  the  triangle  G  H  B  x  2  H; 
moment  of  inertia  of  P3  equal  to  area  of  the  triangle  H  I  C  x  2  H; 
and  moment  of  inertia  of  P4  equal  to  area  of  the  triangle  I  J  D  x  2  H. 
Summing  up  these  values  we  have  the  moment  of  inertia  of  the  sys- 


MOHR'S  METHOD  FOR  MOMENT  OF  INERTIA 


37 


M 


(a) 


-d- 


N 


Mohr's  Method 
I  of  Forces  about  axis  M-N 
=Area  FABGDEcJ-F  x£H 

(b) 
FIG.  23. 

tern  of  forces  equal  to  the  area  of  the  equilibrium  polygon  multiplied 
by  twice  the  pole  distance,  Hf  and 

/  =  area  F  AB  C  D  HJ  F*2H 

To  find  the  radius  of  gyration,  r,  we  use  the  formula 

/  =  R  r* 

In  Fig.  23  the  moment  of  inertia,  I  r,  of  the  resultant  of  the  sys- 
tem of  forces  about  the  axis  M  Nf  can  in  like  manner  be  shown  to  be 
equal  to  area  of  the  triangle  F  H  J  x  2  H. 

If  the  axis  M  N  is  made  to  coincide  with  the  resultant  R  the  mo- 
ment of  inertia  Ic  ^  of  the  system  will  be  equal  to  the  area  of  equi- 
librium polygon  ABCD&X2H.  This  furnishes  a  graphic  proof  for 
the  proposition  that  the  moment  of  inertia,  I,  of  any  system  of  parallel 
forces  about  an  axis  parallel  to  the  resultant  of  the  system  is  equal  to 
the  moment  of  inertia,  I  c  g  ,  of  the  forces  about  an  axis  through  their 
centeroid  plus  the  moment  of  inertia,  Irf  of  their  resultant  about  the 
given  axis. 


It  will  be  seen  from  the  foregoing  discussion  that  the  moment  of 
inertia  of  a  system  of  forces  about  an  axis  through  the  centeroid  of  the 
system  is  a  minimum. 


38  GRAPHIC  STATICS 

Moment  of  Inertia  of  Areas. — The  moment  of  inertia  of  an 
area  about  an  axis  in  the  same  plane  is  equal  to  the  summation  of  the 
products  of  the  differential  areas  which  compose  the  area  and  the 
squares  of  the  distances  of  the  differential  areas  from  the  axis. 

The  moment  of  inertia  of  an  area  about  a  neutral  axis  (axis 
through  center  of  gravity  of  the  area)  is  less  than  that  about  any  parallel 
axis,  and  is  the  moment  of  inertia  used  in  the  fundamental  formula  for 
flexure  in  beams 

M          SI 
M=  — 

where 

M  =  bending  moment  at  point  in  inch-pounds ; 

$  =  extreme  fibre  stress  in  pounds ; 

I  =  moment  of  inertia  of  section  in  inches  to  the  fourth  power; 

c  =  distance  from  neutral  axis  to  extreme  fibre  in  inches. 

An  approximate  value  of  the  moment  of  inertia  of  an  area  may 
be  obtained  by  either  of  the  preceding  methods  by  dividing  the  area 
into  laminae  and  assuming  each  area  to  be  a  force  acting  through  the 
center  of  gravity  of  the  lamina,  the  smaller  the  laminae  the  greater  the 
accuracy.  The  true  value  may  be  obtained  by  either  of  the  above 
methods  if  each  one  of  the  forces  is  assumed  to  act  at  a  distance  from 
the  given  axis  equal  to  the  radius  of  gyration  of  the  area  with  reference 
to  the  axis,  d  =  i/a2-f-  r2,  where  a  is  the  distance  from  the  given  axis  to 
the  center  of  gravity  of  the  lamina  and  r  is  the  radius  of  gyration  of  the 
lamina  about  an  axis  through  its  center  of  gravity.  If  A0  is  the  area 
of  each  lamina  ,the  moment  of  inertia  of  the  lamina  will  be 

/  =  A0  d2  =  A0  a2  +  A0  r*  =  A0a*  +  I  c^ 

which  is  the  fundamental  equation  for  transferring  moments  of  inertia 
to  parallel  axes. 


CHAPTER  VI. 
STRESSES  IN  FRAMED  STRUCTURES. 

Methods  of  Calculation. — The  determination  of  the  reactions  of 
simple  framed  structures  usually  requires  the  use  of  the  three  funda- 
mental equations  of  equilibrium 

2  horizontal  components  of  forces     =  0  (a) 

2  vertical  components  of  forces          =  0  (b) 

2  moments  of  forces  about  any  point  =  0  (c) 

Having  completely  determined  the  external  forces,  the  internal 
stresses  may  be  obtained  by  either  equations  (a)  and  (b)  (resolution), 
or  equation  (c)  (moments).  These  equations  may  be  solved  by 
graphics  or  by  algebra.  There  are,  therefore,  four  methods  of  calcu- 
lating stresses: 

_,  (  Algebraic  Method 

Resolution  of  Forces    <  ~      ..    ,,  .,     , 
(  Graphic  Method 

,,  .  ^  (  Algebraic  Method 

Moments  of  Forces     <  -       ,  .    ,  T    ,     , 
(  Graphic  Method 

The  stresses  in  any  simple  framed  structure  can  be  calculated  by 
using  any  one  of  the  four  methods.  However,  all  the  methods  are 
not  equally  well  suited  to  all  problems,  and  there  is  in  general  one 
method  that  is  best  suited  to  each  particular  problem. 

The  common  practice  of  dividing  methods  of  calculation  of 
stresses  into  analytic  and  graphic  methods  is  meaningless  and  mis- 
leading for  the  reason  that  both  algebraic  and  graphic  methods  are 
analytical,  i.  e.  capable  cf  analysis. 

The  loads  on  trusses  are  usually  considered  as  concentrated  at  the 
joints  in  the  plane  of  the  loaded  chord. 


4° 


STRESSES  IN  FRAMED  STRUCTURES 


Algebraic  Resolution. — In  calculating  the  stresses  in  a  truss  by 
algebraic  resolution,  the  fundamental,  equations  for  equilibrium  for 
translation 

S  horizontal  components  of  forces  =  0  (a) 

S  vertical  components  of  forces        =  0  (b) 

are  applied  (a)  to  each  joint,  or  (b)  to  the  members  and  forces  on  one 
side  of  a  section  cut  through  the  truss. 

(a)  Forces  at  a  Joint. — The  reactions  having  been  found,  the 
stresses  in  the  members  of  the  truss  shown  in  Fig.  24  are  calculated  as 


(Q) 


FIG.  24. 


follows :  Beginning  at  the  left  reaction,  Rlt  we  have  by  applying  equa- 
tions (a)  and  (b) 

\-x  sin  8  —  l-y  sin    oc  =  0  (9) 

\-x  cos  e  —  l-y  cos    oc  —  Rl  =  0  (10) 

The  stresses  in  members  I-JT  and  1-3;  may  be  obtained  by  solving 
equations  (9)  and  (10).  The  direction  of  the  forces  which  rep- 
resent the  stresses  in  amount  will  be  determined  by  the  signs  of  the 
results,  plus  signs  indicating  compression  and  minus  signs  indicating 
tension.  Arrows  pointing  toward  the  joint  indicate  that  the  member 
is  in  compression;  arrows  pointing  away  from  the  joint  indicate  that 
the  member  is  in  tension.  The  stresses  in  the  members  of  the  truss  at 
the  remaining  joints  in  the  truss  are  calculated  in  the  same  way. 

The  direction  of  the  forces  and  the  kind  of  stress  can  always  be 
determined  by  sketching  in  the  force  polygon  for  the  forces  meeting 
at  the  joint  as  in  (c)  Fig.  24. 


ALGEBRAIC  RESOLUTION 


41 


It  will  be  seen  from  the  foregoing  that  the  method  of  algebraic 
resolution  consists  in  applying  the  principle  of  the  force  polygon  to  the 
external  forces  and  internal  stresses  at  each  joint. 

Since  we  have  only  two  fundamental  equations  for  translation 
(resolution)  we  can  not  solve  a  joint  if  there  are  more  than  two  forces 
or  stresses  unknown. 

Where  the  lower  chord  of  the  truss  is  horizontal  as  in  Fig.  25,  we 


Xi 


(b) 


(C) 


FIG.  25. 


have  by  applying  fundamental  equations  (a)  and  (b)  to  the  joint  at 
the  left  reaction 

1-^=  +  ^  sec  0  (U) 

l-ij  =  —  R!  tan  0  (12) 

the  plus  sign  indicating  compression  and  the  minus  sign  tension.  Equa- 
tions (n)  and  (12)  may  be  obtained  directly  from  force  triangle  (c). 
Equations  (n)  and  (12)  are  used  in  calculating  the  stresses  in  trusses 
with  parallel  chords  and  lead  to  the  method  of  coefficients  (Chapter  X). 
(b)  Forces  on  One  Side  of  a  Section. — The  principle  of  resolu- 
tion of  forces  may  be  applied  to  the  structure  as  a  whole  or  to  a  por- 
tion of  the  structure. 

If  the  truss  shown  in  Fig.  26  is  cut  by  the  plane  A  A,  the  internal 
stresses  and  external  forces  acting  on  either  segment,  as  in  (b)  will  be 
in  equilibrium.  The  external  forces  acting  on  the  cut  members  as 
shown  in  (b)  are  equal  to  the  internal  stresses  in  the  cut  members  and 
are  opposite  in  direction. 


42  STRESSES  IN  FRAMED  STRUCTURES 

Applying  equations  (a)  and  (b)  to  the  cut  section 

Z-y  +  2-3  cos    oc  —  2-x  sin  9       =0  (13) 

2-3  sin  oc  —  2-x  cos  6  -f  Bl  —  Pl  =  0  (14) 

Now,  if  all  but  two  of  the  external  forces  are  known,  the  un- 
knowns may  be  found  by  solving  equations  (13)  and  (14).     If  more 


(a) 


(b) 


FIG.  26. 


than  two  external  forces  are  unknown  the  problem  is  indeterminate  as 
far  as  equations  (13)  and  (14)  are  concerned. 


\P    S'     \p    Y<       fait 


(d) 


5tres5  ?-3=5hear!n  Panel  x  sec  6 


FIG.  26a. 


In  the  Warren  truss  in  Fig.  26a  the  stresses  at  a  joint  may  be  cal- 
culated by  completing  the  force  polygon  as  at  the  left  reaction  in  (b) 
Fig.  26a.  Applying  equations  (i)  and  (2)  to  a  section  as  in  (c) 

2,-x  -\-  2-3  sin  0  —  3-3^  =  0 


GRAPHIC  RESOLUTION. 
—  2-3  cos  0  —  P  +  RI =o 


43 


Now,  RI  —  P  =  shear  in  the  panel.  Therefore  the  stress  in  2-3  = — 
(R^  —  P)  sec  6  =  shear  in  panel  Xsec0.  This  analysis  leads  directly 
to  the  method  of  coefficients  as  explained  in  detail  in  Chapter  X. 

Graphic  Resolution. — In  Fig.  27  the  reactions  R1  and  R2  are 
found  by  means  of  the  force  and  equilibrium  polygons  as  shov/n  in  (b) 
and  (a).  The  principle  of  the  force  polygon  is  then  applied  to  each 


P. 


lo1      20r      30' 


Scale  of  Lengths 

IT 


Joint  Lo 


FIG.  27. 


44 


STRESSES  IN  FRAMED  STRUCTURES. 


joint  of  the  structure  in  turn.  Beginning  at  the  joint  L0  the  forces 
are  shown  in  (c),  and  the  force  triangle  in  (d).  The  reaction  ^  is 
known  and  acts  up,  the  upper  chord  stress  i-x  acts  downward  to 
the  left,  and  the  lower  chord  stress  i-y  acts  to  the  right,  closing  the 
polygon.  Stress  \-x  is  compression  and  stress  i-y  is  tension,  as 
can  be  seen  by  applying  the  arrows  to  the  members  in  (c).  The 
force  polygon  at  joint  U^  is  then  constructed  as  in  (f).  Stress  \-x 
acting  toward  joint  Ui  and  load  Pl  acting  downward  are  known,  and 


U, 


Joint  Lt 


FIG.  2/a. 


Stress  Diagram 


stresses  1-2  and  2,-x  are  found  by  completing  the  polygon.  Stresses 
2,-x  and  1-2  are  compression.  The  force  polygons  at  joints  Lt  and  Uz 
are  constructed,  in  the  order  given,  in  the  same  manner.  The  known 
forces  at  any  joint  are  indicated  in  direction  in  the  force  polygon  by 
double  arrows,  and  the  unknown  forces  are  indicated  in  direction  by 
single  arrows. 

The  stresses  in  the  members  of  the  right  segment  of  the  truss  are 
the  same  as  in  the  left,  and  the  force  polygons  are,  therefore,  not  con- 
structed for  the  right  segment.  The  force  polygons  for  all  the  joints 


ALGEBRAIC  MOMENTS. 


45 


of  the  truss  are  grouped  into  the  stress  diagram  shown  in  (k).  Com- 
pression in  the  stress  diagram  and  truss  is  indicated  by  arrows  acting 
toward  the  ends  of  the  stress  lines  and  toward  the  joints,  respectively, 
and  tension  is  indicated  -by  arrows  acting  away  from  the  ends  of  the 
stress  lines  and  away  from  the  joints,  respectively.  The  first  time  a 
stress  is  used  a  single  arrow,  and  the  second  time  the  stress  is  used  a 
double  arrow  is  used  to  indicate  direction.  The  stress  diagram  in  (k) 
Fig.  27  is  called  a  Maxwell  diagram  or  a  reciprocal  polygon  diagram. 
The  notation  used  is  known  as  Bow's  notation.  The  method  of  graphic 
resolution  is  the  method  most  commonly  used  for  calculating  stresses  in 
roof  trusses  and  simple  framed  structures  with  inclined  chords. 

Warren  Bridge  Truss. — In  Fig.  27a  the  dead  load  stresses  in  a 
Warren  bridge  truss  loaded  on  the  lower  chord,  are  calculated  by  the 
method  of  graphic  resolution.  In  the  stress  diagram  the  loads  are 
laid  off  from  the  bottom  upwards.  The  details  of  the  solution  can 
easily  be  followed  by  reference  to  Fig.  27a  and  Fig.  27.  It  will  be  seen 
that  the  upper  chord  of  the  truss  is  in  compression,  while  the  lower 
chord  is  in  tension. 

Algebraic  Moments. — The  reactions  may  be  found  by  applying 
the  fundamental  equations  of  equilibrium  to  the  structure  as  a  whole. 
In  the  truss  in  (a)  Fig.  28  by  taking  moments  about  the  right  reaction 
we  have 


(C) 


FIG.  28. 


46  STRESSES  IN  FRAMED  STRUCTURES. 


To  find  the  stresses  in  the  members  of  the  truss  in  (a)  Fig.  28, 
proceed  as  follows:  Cut  the  truss  by  means  of  plane  AA,  as  in  (b), 
and  replace  the  stresses  in  the  members  cut  away  with  external  forces. 
These  forces  are  equal  to  the  stresses  in  the  members  in  amount,  but 
opposite  in  direction,  and  produce  equilibrium. 

To  obtain  stress  4-^  take  center  of  moments  at  L2,  and  take  mo- 
ments of  external  forces 

4-;r  x  a  -f  Pl  x  d  —  R^  x  2d=  o 


,  x  2    —    .  , 

4-vF  =  -       -  =  -  (compression) 

To  obtain  stress  in  4-5  take  center  of  moments  at  L0,  and  take 
moments  of  external  forces 

4-5  X  b  —  2Pj  x  f^=  o 

$P.d 
4-5  =  =—-  (tension) 

To  obtain  the  stress  in  5-3;  take  center  of  moments  at  joint  Us  in 
(c),  and  take  moments  of  external  forces 


To  Determine  Kind  of  Stress.— If  the  unknown  external  force  is 
always  taken  as  acting  from  the  outside  toward  the  cut  section,  i.  e., 
is  always  assumed  to  cause  compression,  the  sign  of  the  result  will  indi- 
cate the  kind  of  stress.  A  plus  sign  will  indicate  that  the  assumed  direc- 
tion was  correct  and  that  the  stress  is  compression,  while  a  minus  sign 
will  indicate  that  the  assumed  direction  was  incorrect  and  that  the  stress 
is  tension. 

In  calculating  stresses  by  algebraic  moments,  therefore,  always 
observe  the  following  rule : — 

Assume  the  unknown  external  force  as  acting  from  the  outside 
toward  the  cut  section ;  a  plus  sign  for  the  result  will  then  show  that 
the  stress  in  the  member  is  compression,  and  a  minus  sign  will  indicate 
that  the  stress  in  the  member  is  tension. 


GRAPHIC  MOMENTS. 


46a 


The  stresses  in  the  web  members  3-4,  2-3,  1-2,  are  found  by 
taking  moments  about  joint  L0  as  a  center.  The  stresses  in  ^-3  and 
y-i  are  found  by  taking  moments  about  joints  U2  and  U19  respectively; 
and  the  stresses  in  A'-2  and  x-\  are  found  by  taking  moments  about 
joint  Lt. 

The  method  of  algebraic  moments  is  the  most  common  method 
used  for  calculating  the  stresses  in  bridge  trusses  with  inclined  chords 
and  similar  frameworks  which  carry  moving  loads. 

Stresses  in  a  Bridge  Truss. — Calculate  reaction  R19  Fig.  28a,  by 
taking  moments  of  the  vertical  forces  about  joints  L0'.  Then  R±y(L 


=  6P-L/2,  and  R1  =  ^P  =  R2.  To  calculate  the  stress  in  any  member 
in  the  truss,  pass  a  section  cutting  the  member  in  which  the  stress  is 
required,  and  cutting  away  the  truss  on  one  side  of  the  section.  The 
stresses  in  the  members  cut  away  are  assumed  as  replaced  by  external 
forces  acting  in  the  line  of  the  member  and  equal  to  the  stresses  in 
amount. 

To  calculate  the  stresses  take  the  center  of  moments  so  that  there 
will  be  but  one  unknown  stress.     The  solution  of  the   equation  of 


46b 


STRESSES  IN  FRAMED  STRUCTURES. 


moments  about  this  center  of  moments  will  give  the  required  stress. 
To  calculate  the  stress  in  4-5  in  (b)  Fig.  28a,  pass  the  section  a-a, 
cutting  away  the  right  side  of  the  truss,  and  take  the  center  of  moments 
at  the  intersection  of  the  top  and  bottom  chords.  Now  5-.*  and  4~y 
act  through  the  center  of  moments  and  produce  no  moment.  The 
moment  of  the  stress  in  4-5  acting  from  the  outside  toward  the  cut 
section  with  an  arm  c,  holds  in  equilibrium  the  reaction  Rlt  and  the  two 
loads,  P.  The  sign  of  the  result  will  determine  the  kind  of  stress, 
minus  for  tension  and  plus  for  compression.  To  calculate  the  stress  in 
the  top  chord  U2U3,  pass  section  b-b  in  (c)  and  take  moments  about 
joint  L3. 

Graphic  Moments. — The  bending  moment  at  any  point  in  a  truss 
may  be  found  by  means  of  a  force  and  equilibrium  polygon  as  in  (b) 


and  (a)  Fig.  29.  To  determine  the  stress  in  ^-x  cut  section  A  A  and 
take  moments  about  joint  L2  as  in  Fig.  28.  The  moment  of  the  exter- 
nal forces  on  the  left  of  L2  will  be  M2  =  —  Hy2,  and  stress 


4-*=  -9=.. 

a  a 

To  obtain  stress  in  4-5  take  center  of  moments  at  joint  L0,  and 
stress 


~-~b~-    ~r 

To  obtain  stress  in  5-37  take  center  of  moments  at  joint  U3,  and 
stress 

^      fyi 
h 


h 


The  method  of  graphic  moments  is  principally  used  to  explain 
other  methods  and  is  little  used  as  a  direct  method  of  calculation. 


CHAPTER  VII. 
STRESSES  IN  SIMPLE  ROOF  TRUSSES. 

Loads. — The  stresses  in  roof  trusses  are  due  (i)  to  the  dead  load. 
(2)  the  snow  load,  (3)  the  wind  load,  and  (4)  concentrated  and  moving 
loads.  The  stresses  due  to  dead,  snow,  wind  and  concentrated  loads 
will  be  discussed  in  this  chapter  in  the  order  given. 

Dead  Load  Stresses. — The  dead  load  is  made  up  of  the  weight 
of  the  truss  and  roof  covering  and  is  usually  considered  as  applied  at 
the  panel  points  of  the  upper  chord  in  computing  stresses  in  roof 
trusses.  If  the  purlins  do  not  come  at  the  panel  points,  the  upper  chord 
will  have  to  be  designed  for  both  direct  stress  and  stress  due  to  flexure. 

The  stresses  in  a  Fink  truss  due  to  dead  load  are  calculated  by 
graphic  resolution  in  Fig.  30. 


FIG.  30. 


48  STRESSES  IN  ROOF  TRUSSES 

The  loads  are  laid  off,  the  reactions  found,  and  the  stresses  calcu- 
lated beginning  at  joint  L0,  as  explained  in  Fig.  27.  The  stress  diagram 
for  the  right  half  of  the  truss  need  not  be  drawn  where  the  truss  and 
loads  are  symmetrical  as  in  Fig.  30;  however  it  gives  a  check  on  the 
accuracy  of  the  work  and  is  well  worth  the  extra  time  required.  The 
loads  P1  on  the  abutments  have  no  effect  on  the  stresses  in  the  truss 
and  may  be  omitted  in  this  solution. 

In  calculating  the  stresses  at  joint  P3,  the  stresses  in  the  members 
3-4,  4-5  and  ^r-5  are  unknown,  and  the  solution  appears  to  be  in- 
determinate. The  solution  is  easily  made  by  cutting  out  members  4-5 
and  5-6,  and  replacing  them  with  the  dotted  member  shown.  The 
stresses  in  the  members  in  the  modified  truss  are  now  obtained  up  to 
and  including  stresses  6-jf  and  6-7.  Since  the  stresses  6-,r  and 
6-7  are  independent  of  the  form  of  the  framework  to  the  left,  as  can 
easily  be  seen  by  cutting  a  section  through  the  members  6-;r,  6-7 
and  7-^,  the  solution  can  be  carried  back  and  the  apparent  ambiguity 
removed.  The  ambiguity  can  also  be  removed  by  calculating  the  stress 
in  j-y  by  algebraic  moments  and  substituting  it  in  the  stress  diagram. 
It  will  be  noted  that  all  top  chord  members  are  in  compression  and  all 
bottom  chord  members  are  in  tension. 

The  dead  load  stresses  can  also  be  calculated  by  any  of  the  three 
remaining  methods,  as  previously  described. 

Dead  and  Ceiling  Load  Stresses. — The  stresses  in  a  triangular 
Pratt  truss  due  to  dead  and  ceiling  loads,  are  calculated  by  graphic 
resolution  in  Fig.  31. 

For  simplicity  the  stresses  are  shown  for  one  side  only.  The  re- 
action RI  is  equal  to  one-half  of  the  entire  load  on  the  truss.  The  solu- 
tion will  appear  more  clear  when  it  is  noted  that  the  stress  diagram 
shown  consists  of  two  diagrams,  one  due  to  loads  on  the  upper  chord 
and  the  other  due  to  loads  on  the  lower  chord,  combined  in  one,  the 
loads  in  each  case  coming  between  the  stresses  in  the  members  on  each 
side  of  the  load.  The  top  chord  loads  are  laid  off  in  order  downward, 
while  the  bottom  chord  loads  are  laid  off  in  order  upward. 


SNOW  LOAD  STRESSES 


49 


O  5          10'         15* 


DEAD  AND  CEILING  LOADS 


FIG.  31. 

Snow  Load  Stresses. — Large  snow  storms  nearly  always  occur 
in  still  weather,  and  the  maximum  snow  load  will  therefore  be  a  uni- 
formly distributed  load.  A  heavy  wind  may  follow  a  sleet  storm  and 
a  snow  load  equal  to  the  minimum  given  in  Fig.  4  should  be  considered 
as  acting  at  the  same  time  as  the  wind  load.  The  stresses  due  to  snow 
load  are  found  in  the  same  manner  as  the  dead  load  stresses. 

Wind  Load  Stresses. — The  stresses  in  trusses  due  to  wind  load 
will  depend  upon  the  direction  and  intensity  of  the  wind,  and  the  con- 
dition of  the  end  supports.  The  wind  is  commonly  considered  as  act- 
ing horizontally,  and  the  normal  component,  as  determined  by  one  of 
the  formulas  in  Fig.  6,  is  taken. 

The  ends  of  the  truss  may  (i)  be  rigidly  fixed  to  the  abutment 
walls,  (2)  be  equally  free  to  move,  or  (3)  may  have  one  end  fixed  and 
the  other  end  on  rollers.  When  both  ends  of  the  truss  are  rigidly 
fixed  to  the  abutment  walls  (i)  the  reactions  are  parallel  to  each  other 


5° 


STRESSES  IN  ROOF  TRUSSES 


and  to  the  resultant  of  the  external  loads;  where  both  ends  of  the 
truss  are  equally  free  to  move  (2)  the  horizontal  components  of  the 
reactions  are  equal;  and  where  one  end  is  fixed  and  the  other  end  is 
on  frictionless  rollers  (3)  the  reaction  at  the  roller  end  will  always 
be  vertical.  Either  case  (i)  or  case  (3)  is  commonly  assumed  in  cal- 
culating wind  load  stresses  in  trusses.  Case  (2)  is  the  condition  in  a 
portal  or  framed  bent.  The  vertical  components  of  the  reactions  are 
independent  of  the  condition  of  the  ends. 

Wind  Load  Stresses:  No  Rollers. — The  stresses  due  to  a  nor- 
mal wind  load,  in  a  Fink  truss  with  both  ends  fixed  to  rigid  walls,  are 
calculated  by  graphic  resolution  in  Fig.  32.  The  reactions  are  parallel 


10'       15* 


Wind  Load 
No  Rollers  ,'' 


20OO  4OOO     6000 


FIG.  32. 


and  their  sum  equals  sum  of  the  external  loads;  they  are  found  by 
means  of  force  and  equilibrium  polygons  as  in  Fig.  15  and  'Fig.  27 


WIND  LOAD  STRESSES  51 

The  stress  diagram  is  constructed  in  the  same  manner  as  that  for  dead 
loads.  Heavy  lines  in  truss  and  stress  diagram  indicate  compression, 
and  light  lines  indicate  tension. 

The  ambiguity  at  joint  Ps  is  removed  by  means  of  the  dotted  mem- 
ber as  in  the  case  of  the  dead  load  stress  diagram.  It  will  be  seen  that 
there  are  no  stresses  in  the  dotted  web  members  in  the  right  segment 
of  the  truss.  It  is  necessary  to  carry  the  solution  entirely  through  the 
truss,  beginning  at  the  left  reaction  and  checking  up  at  the  right  re- 
action. It  will  be  seen  that  the  load  P±  has  no  effect  on  the  stresses  in  the 
truss  in  this  case. 

Wind  Load  Stresses:  Rollers. — Trusses  longer  than  70  feet 
are  usually  fixed  at  one  end,  and  are  supported  on  rollers  at  the  other 
end.  The  reaction  at  the  roller  end  is  then  vertical — the  horizontal  com- 
ponent of  the  external  wind  force  being  all  taken  by  the  fixed  end.  The 
wind  may  come  on  either  side  of  the  truss  giving  rise  to  two  conditions ; 
(i)  rollers  leeward  a.n<]  (2)  rollers  windward,  each  requiring  a  separate 
solution. 

Rollers  Leeward  -The  wind  load  stresses  in  a  triangular  Pratt 
truss  with  rollers  under  the  leeward  side  are  calculated  by  graphic 
resolution  in  Fig.  33. 

The  reactions  in  Fig.  33  were  first  determined  by  means  of  force 
and  equilibrium  polygons,  on  the  assumption  that  they  were  parallel  to 
each  other  and  to  the  resultant  of  the  external  loads.  Then  since  the 
reaction  at  the  roller  end  is  vertical  and  the  horizontal  component  at  the 
fixed  end  is  equal  to  the  horizontal  component  of  the  external  wind 
forces,  the  true  reactions  were  obtained  by  closing  the  force  polygon. 

In  order  that  the  truss  be  in  equilibrium  under  the  action  of  the 
three  external  forces  Rlt  R2  and  the  resultant  of  the  wind  loads, 
the  three  external  forces  must  meet  in  a  point  if  produced.  This  fur- 
nishes a  method  for  determining  the  reactions,  where  the  direction  and 
line  of  action  of  one  and  a  point  in  the  line  of  action  of  the  other  are 
known,  providing  the  point  of  intersection  of  the  three  forces  comes 
within  the  limits  of  the  drawing  board. 


52 


STRESSES  IN  ROOF  TRUSSES 


Wind  Load 
Rollers  Lee 


FIG.  33- 

The  stress  diagram  is  constructed  in  the  same  way  as  the  stress 
diagram  for  dead  loads.  It  will  be  seen  that  the  load  P±  has  no  effect 
on  the  stresses  in  the  truss  in  this  case.  Heavy  lines  in  truss  and  stress 
diagram  indicate  compression  and  light  lines  indicate  tension. 

Rollers  Windward. — The  wind  load  stresses  in  the  same  trian- 
gular Pratt  truss  as  shown  in  Fig.  33,  with  rollers  under  the  windward 
side  of  the  truss  are  calculated  by  graphic  resolution  in  Fig.  34. 

The  true  reactions  were  determined  directly  by  means  of  force  and 
equilibrium  polygons  as  in  Fig.  16.  The  direction  of  the  reaction  R^ 
is  known  to  be  vertical,  but  the  direction  of  the  reaction  R2  is  unknown, 
the  only  known  point  in  its  line  of  action  being  the  right  abutment.  The 
equilibrium  polygon  is  drawn  to  pass  through  the  right  abutment  and 
the  direction  of  the  right  reaction  is  determined  by  connecting  the 


CONCENTRATED  LOAD  STRESSES 

0*       10'     20'     30* 


53 


-^  \ 

Wind  Load 
Rollers  Wind 


point  of  intersection  of  the  vertical  reaction  R^  and  the  line  drawn 
through  o  parallel  to  the  closing  line  of  the  equilibrium  polygon,  with 
the  lower  end  of  the  load  line. 

Since  the  vertical  components  of  the  reactions  are  independent  of 
the  conditions  of  the  ends  of  the  truss,  the  vertical  components  of  the 
reactions  in  Fig.  33  and  Fig.  34  are  the  same.  It  will  be  seen  that  the 
load  P!  produces  stress  in  the  members  of  the  truss  with  rollers  wind- 
ward. If  the  line  of  action  of  R2  drops  below  the  joint  P5  the  lower 
chord  of  the  truss  will  be  in  compression,  as  will  be  seen  by  taking 
moments  about  P5. 

Concentrated  Load  Stresses. — The  stresses  in  a  Fink  truss  due 
to  unequal  crane  loads  are  calculated  by  graphic  resolution  in  Fig.  35. 

The  reactions  were  found  by  means  of  force  and  equilibrium  poly- 
gons. The  truss  is  reduced  to  three  triangles  for  the  loading  shown. 
The  solution  of  this  problem  is  similar  to  that  for  ceiling  loads  in  Fig. 


54 


STRESSES  IN  ROOF  TRUSSES 


31.  The  moving  crane  trolley  will  produce  maximum  moment  when 
it  is  at  the  center  of  the  truss,  and  this  case  should  be  investigated  in 
solving  the  problem. 


10'         15' 


2OOO        4OOO          6OOO 


FIG.  35. 

The  method  of  graphic  resolution  is  commonly  used  for  calculat- 
ing the  stresses  in  roof  trusses  and  similar  structures.  For  examples 
of  the  calculations  of  stresses  in  trusses  by  algebraic  resolution,  al- 
gebraic and  graphic  moments,  see  Chapter  X. 


CHAPTER  VIII. 
SIMPLE  BEAMS. 

Reactions. — The  reactions  of  beams  may  be  found  by  the  use 
of  the  force  and  equilibrium  polygon  as  shown  in  Chapter  V.  As  a  sec- 
ond example  let  it  be  required  to  find  the  reactions  of  the  overhanging 
beam  shown  in  Fig.  36. 


(a) 


i-Y-r 


R2 


%-A 


FIG.  36. 


--^--H « 


(b) 


Construct  a  force  polygon  with  pole  o,  as  in  (b),  and  draw  an  equi- 
librium polygon,  as  in  (a).  The  ray  o  d  drawn  parallel  to  the  closing 
line  o  dm  (a)  determines  the  reactions.  In  this  case  reaction  R^  .is 
negative.  It  should  be  noted  that  the  closing  line  in  an  equilibrium 
polygon  must  have  its  ends  on  the  two  reactions. 

The  ordinate  to  the  equilibrium  polygon  at  any  point  multiplied 
by  the  pole  distance,  H,  will  give  the  bending  moment  in  the  beam  at  a 
point  immediately  above  it. 


56  SIMPLE  BEAMS 

Moment  and  Shear  in  Beams :  Concentrated  Loads. — The  bend- 
ing moment  in  the  beam  shown  in  Fig.  37  may  be  found  by  constructing 
the  force  polygon  (a)  and  equilibrium  polygon  (b)  as  shown. 


t 

PZ 

h  r   Th 

1         i                     Pi 

\ 

b\ 

x^v      \ 

x  -     \ 
v.    \ 

f                            XXXN^ 

jl 

!             !      f 

i 

i 
!  o       \- 

a 

rlf 

ill 
0 

Morr 

(b) 

ent  Dia 

yg    R'  ! 

grarH     R2^f3 

K 

]      i.ilj 

IB 

c"    ^y'  \ 

•gpr*-* 

<*       (a) 

Force  Polygon 

i 
i 
i 
i 

Ri 
i 

t 

"  '  '-» 

1 

Pi 

(        V 

"  ~X 

i 

A 

Illinium 

-R2 

(c) 
Shear  Diagram 

i 
P3 

A 

B* 

FIG.  37. 

The  bending  moment  at  any  point  is  then  equal  to  the  ordinate 
to  the  equilibrium  polygon  at  that  point  multiplied  by  the  pole  distance, 
H.  The  ordinate  is  to  be  measured  to  the  same  scale  as  the  beam,  and 
the  pole  distance,  H,  is  to  be  measured  to  the  same  scale  as  the  loads  in 
the  force  polygon.  The  ordinate  is  a  distance  and  the  pole  distance 
is  a  force. 

Or,  if  the  scale  to  which  the  beam  is  laid  off  be  multiplied  by  the 
pole  distance  measured  to  the  scale  of  the  loads,  and  this  scale  be  used 
in  measuring  the  ordinates,  the  ordinates  will  be  equal  to  the  bending 
moments  at  the  corresponding  points.  This  is  the  same  as  making  the 
pole  distance  equal  to  unity.  Diagram  (b)  is  called  a  moment  diagram. 

Between  the  left  support  and  the  first  load  the  shear  is  equal  to 


MOMENT  AND  SHEAR  IN  BEAMS  57 

R!  ;  between  the  loads  F1  and  P2  the  shear  equals  R^  —  Px  ;  between 
the  loads  F2  and  P3  the  shear  equals  R^  —  Px  —  F2  5  between  the  loads 
P3  and  P4  the  shear  equals  7^  —  Px  —  P2  —  P3  ;  and  between  load  F4 
and  the  right  reaction  the  shear  equals  R-L  —  Fx  —  P2  —  P3  —  F4  =  — 
R2.  At  load  P2  the  shear  changes  from  positive  to  negative.  Diagram 
(c)  is  called  a  shear  diagram.  It  will  be  seen  that  the  maximum 
ordinate  in  the  moment  diagram  comes  at  the  point  of  zero  shear. 

The  bending  moment  at  any  point  in  the  beam  is  equal  to  the 
algebraic  sum  of  the  shear  areas  on  either  side  of  the  point  in  question. 
From  this  we  see  that  the  shear  areas  on  each  side  of  P2  must  be  equal. 
This  property  of  the  shear  diagram  depends  upon  the  principle  that  the 
bending  moment  at  any  point  in  a  simple  beam  is  the  definite  integral  of 
the  shear  between  either  point  of  support  and  the  point  in  question. 
This  will  be  taken  up  again  in  the  discussion  of  beams  uniformly  loaded 
which  will  now  be  considered. 

Moment  and  Shear  in  Beams:  Uniform  Loads.  —  In  the  beam 
loaded  with  a  uniform  load  of  w  Ibs.  per  lineal  foot  shown  in  Fig.  38, 
the  reaction  Rt  =  R2  =  j£  w  L.  At  a  distance  x  from  the  left  support, 
the  bending  moment  is 


which  is  the  equation  of  a  parabola. 

The  parabola  may  be  constructed  by  means  of  the.  force  and  equi- 
librium polygons  by  assuming  that  the  uniform  load  is  concentrated  at 
points  in  the  beam,  as  is  assumed  in  a  bridge  truss,  and  drawing  the 
force  and  equilibrium  polygons  in  the  usual  way,  as  in  Fig.  38.  The 
greater  the  number  of  segments  into  which  the  uniform  load  is  divided 
the  more  nearly  will  the  equilibrium  polygon  approach  the  bending 
moment  parabola. 

The  parabola  may  be  constructed  without  drawing  the  force  and 
equilibrium  polygons  as  follows  :  Lay  off  ordinate  m  n  —  n  p  =  bend- 
ing moment  at  center  of  beam  =  %  w  L2.  Divide  a  p  and  b  p  into  the 
same  number  of  equal  parts  and  number  them  as  shown  in  (b).  Join 
the  points  with  like  numbers  by  lines,  which  will  be  tangents  to  the 


SIMPLE;  BEAMS 


Load  =  w  Ibs-  per  lin-  ft. 

| 


f*l 


(c) 

Shear   Diagram 

FiG.  38. 

required  parabola.  It  will  be  seen  in  Fig.  38  that  points  on  the  parabola 
are  also  obtained. 

The  shear  at  any  point  x,  will  be 

S=Rl  —  wx  =  *  wL  —  wx  =  w  (-—  x} 

which  is  the  equation  of  the  inclined  line  shown  in  (c)  Fig.  38.  The 
shear  at  any  point  is  therefore  represented  by  the  ordinate  to  the  shear 
diagram  at  the  given  point. 

Property  of  the  Shear  Diagram. — Integrating   the    equation     for 
shear  between  the  limits,  x  =  o  and  x  =  x  we  have 

T~-x\dx 


which  is  the  equation  for  the  bending  moment  at  any  point,  x,  in  the 
beam,  and  is  also  the  area  of  the  shear  diagram  between  the  limits 
given.  From  this  we  see  that  the  bending  moment  at  any  point  in  a 
simple  beam  uniformly  loaded  is  equal  to  the  area  of  the  shear  dia- 
gram to  the  left  of  the  point  in  question.  The  bending  moment  is  also 
equal  to  the  algebraic  sum  of  the  shear  areas  on  either  side  of  the  point. 


CHAPTER  IX. 


MOVING  LOADS  ON  BEAMS. 

Uniform  Moving  Loads. — Let  the  beam  in  Fig.  39  be  loaded  with 
a  uniform  load  of  p  Ibs.  per  lineal  foot,  which  can  be  moved  on  or  off 
the  beam. 


Uniform  Moving  Load 
=  p  Ibs- per  lin-fr- 


(a)    Maximum  Positive  Shear 
Load  moving  off  To  the  right 


(b) 

Maximum  Negative  Shear 
Load  moving  off  to  the   left 

FIG.  39. 

To  find  the  position  of  the  moving  load  that  will  produce  a  max- 
imum moment  at  a  point  a  distance  a  from  the  left  support,  proceed 
as  follows :  Let  the  end  of  the  uniform  load  be  at  a  -distance  x  from 

o  we  have 


the  left  reaction.    Then  taking  moments  about 

/   T    ^__    -,\  2 

^1     =  t.        T P 


and  the  moment  at  the  point  whose  abscissa  is  a  will  be 


(15) 


(16) 


60  MOVING  LOADS  ON  BEAMS 

Differentiating   (16)   and  placing  derivative  of  M  with  respect  to  x 
equal  to  zero,  we  have  after  solving 

x=o  (17) 

Therefore  the  maximum  moment  at  any  point  in  a  beam  will  occur 
when  the  beam  is  fully  loaded. 

The  bending  moment  diagram  for  a  beam  loaded  with  a  uniform 
moving  load  is  constructed  as  in  Fig.  38. 

To  find  the  position  of  the  moving  load  for  maximum  shear  at  any 
point  in  a  beam  loaded  with  a  moving  uniform  load,  proceed  as  fol- 
lows :  The  left  reaction  when  the  end  of  the  moving  load  is  at  a  dis- 
tance x  from  the  left  reaction,  will  be 

*i==(-^-  p 


and  the  shear  at  a  point  at  a  distance  a  from  the  left  reaction  will  be 
S=Ri—(a-x)p  =  ^-^?p-(a--x)p  (18) 

which  is  the  equation  of  a  parabola. 

By  inspection  it  can  be  seen  that  S  will  be  a  maximum  when 
a  =  x.  The  maximum  shear  at  any  point  in  a  beam  will  therefore 
occur  at  the  end  of  the  uniform  moving  load,  the  beam  being  fully 
loaded  to  the  right  of  the  point  as  in  (a)  Fig.  39  for  maximum  positive 
shear,  and  fully  loaded  to  the  left  of  the  point  as  in  (b)  Fig.  39  for 
maximum  negative  shear. 

If  the  beam  is  assumed  to  be  a  cantilever  beam  fixed  at  A,  and 
loaded  with  a  stationary  uniform  load  equal  to  p  Ibs.  per  lineal  foot,  and 
an  equilibrium  polygon  be  drawn  with  a  force  polygon  having  a  pole 
distance  equal  to  length  of  span,  L,  the  parabola  drawn  through  the 
points  in  the  equilibrium  polygon  will  be  the  maximum  positive  shear 
diagram,  (a)  Fig.  39.  The  ordinate  at  any  point  to  this  shear  diagram 
will  represent  the  maximum  positive  shear  at  the  point  to  the  same 
s^ale  as  the  loads  (for  the  application  of  this  principal  to  bridge  trusses 
see  Fig.  50,  Chapter  X). 


CONCENTRATED  MOVING  LOADS  61 

Concentrated  Moving  Loads. — Let  a  beam  be  loaded  with  con- 
centrated moving  loads  at  fixed  distances  apart  as  shown  in  Fig.  40. 

(••-^ 

Pa)co.r5)        ra 


R,4  ,--a~*-b-*-   c  --i       *R 

£  ---    x    ---  »|          K-  ^  --(_*_)  -_-_-  -4 

FIG.  40. 

To  find  the  position  of  the  loads  for  maximum  moment  and  the 
amount  of  the  maximum  moment,  proceed  as  follows:  The  load  P2 
will  be  considered  first.  Let  x  be  the  distance  of  the  load  P2 
from  the  left  support  when  the  loads  produce  a  maximum  moment  un- 
der load  P2. 

Taking  moment:;  about  R2  we  have 

Pl  (L  — 


and  the  bending  moment  under  load  P2  will  be 

M=Rlx—Pl  a 

7>3+  P.)  +  x  (/>  a-P3  b—P.  (b  +  c)  ) 


Differentiating  (20)  we  have 
d  M  _(L  —  1x]  (Pl+Pt 


d  x  L 

and  solving  (21)  for  x  we  have 

~. _j ^-**  ' 

—    2  ^^      ^  (P     I   p   -4-P     I    D  \ 

Now  P!  a  —  P&  b  —  F4  (b  +  c),  is  the  static  moment  of  the  loads 
about  F2  and 


62  MOVING  LOADS  ON  BEAMS 

distance  from  *  to 


center  of  the  gravity  of  all  the  loads. 

Therefore,  for  a  maximum  moment  under  load  P2,  it  must  be  as 
far  from  one  end  as  the  center  of  gravity  of  all  the  loads  is  from  the 
other  end  of  the  beam,  Fig.  40. 

The  above  criterion  holds  for  all  the  loads  on  the  beam.  The  only 
way  to  find  which  load  produces  the  greatest  maximum  is  to  try  each 
one,  however,  it  is  usually  possible  to  determine  by  inspection  which 
load  will  produce  a  maximum  bending  moment.  For  example  the 
maximum  moment  in  the  beam  in  Fig.  40  will  certainly  come  under 
the  heavy  load  P2.  The  above  proof  may  be  generalized  without  diffi- 
culty and  the  criterion  above  shown  to  be  of  general  application. 

For  two  equal  loads  ~P  =  P  at  a  fixed  distance,  a,  apart  as  in  the 
case  of  a  traveling  crane,  Fig.  41,  the  maximum  moment  will  occur 
under  one  of  the  loads  when 

_A     JL 

:  2  ~~~T 

K -----  a -->» 

s^ 


(?) 


R 

t- 

L 

-a 

i 

j^C-G.of 

Loads 

4 

'd 

A- 

**          £ 

4 

' 

L 

<                       L 

i 

?.:;.::: 

i 

FIG.  41. 
Taking  moments  about  the  right  reaction  we  have 


L 
and  the  maximum  bending  moment  is 


(24) 

-I  J-f 


CONCENTRATED  MOVING  LOADS  63 

There  will  be  a  maximum  moment  when  either  of  the  loads  satis- 
fies the  above  criterion,  the  bending  moments  being  equal. 

By  equating  the  maximum  moment  above  to  the  moment  due  to 
a  single  load  at  the  center  of  the  beam,  it  will  be  found  that  the  above 
criterion  holds  only  when 

a  <  0.586  L 

Where  two  unequal  moving  loads  are  at  a  fixed  distance  apart  the 
greater  maximum  bending  moment  will  always  come  under  the  heavier 
3ad. 

The  maximum  end  shear  at  the  left  support  for  a  system  of  con- 
centrated loads  on  a  simple  beam,  as  in  Fig.  40,  will  occur  when  the 
left  reaction,  Rlt  is  a  maximum.  This  will  occur  when  one  of  the  wheels 
is  infinitely  near  the  left  abutment  (usually  said  to  be  over  the  left 
abutment).  The  load  which  produces  maximum  end  shear  can  be 
easily  found  by  trial. 

The  maximum  shear  at  any  point  in  the  beam  will  occur  when 
one  of  the  loads  is  over  the  point.  The  criterion  for  determining-  which 
load  will  cause  a  maximum  shear  at  any  point,  x,  in  a  beam  will  now 
be  determined. 

In  Fig.  40,  let  the  total  load  on  the  beam,  P1  +  F2  +  F3  +  P4  = 
Wt  and  let  x  be  the  distance  from  the  left  support  to  the  point  at  which 
we  wish  to  determine  the  maximum  shear. 

When  load  Px  is  at  the  point,  the  shear  will  be  equal  to  the  left 
reaction,  which  is  found  by  substituting  x  -\-  a  for  x  in  (19)  to  be 

(L-X-a)  W+Pla-P36-P4(6  +  c) 


and  when  P2  is  at  the  point  the  shear  will  be 

(L  —  x)  W+l 
o2  =  — 

Subtracting  S2  from  5\  we  have 


(L  —  x)  W+Pla-P3d-P<(t>  + 
L 


P^L-Wa 


64  MOVING  LOADS  ON  BEAMS 

Now  Si  will  be  greater  than  $2  if  P±  L  is  greater  than  W  a,  or  if 

£i^>  w 

#    ^ 

The  criterion  for  maximum  shear  at  any  point  therefore  is  as 
follows : 

The  maximum  positive  shear  in  any  section  of  a  beam  occurs  when 

P  T 

the  foremost  load  is  at  the  section,  provided  W  is  not  greater  than  — - — 

P  7" 

If  W  is  greater  than  — ^— ,  the  greatest  shear  will  occur  when  some 

succeeding  load  is  at  the  point. 

Having  determined  the  position  of  the  moving  loads  for  maxi- 
mum moment  and  maximum  shear,  the  amount  of  the  moment  and 
shear  can  be  obtained  as  in  the  case  of  beams  loaded  with  stationary 
loads. 


CHAPTER  X. 
STRESSES  IN  BRIDGE  TRUSSES. 

Method  of  Loading. — The  loads  on  highway  bridges,  and  in 
many  cases  on  railway  bridges  as  well,  are  assumed  to  be  concentrated 
at  the  joints  of  the  loaded  chord,  and  if  the  panels  of  the  truss  are  equal 
the  joint  loads  are  equal.  The  assumption  of  joint  loads  simplifies  the 
solution  and  gives  values  for  the  stresses  that  are  on  the  safe  side.  Equal 
joint  loads  will  be  assumed  in  this  discussion. 

Algebraic  Resolution.* — Let  the  Warren  truss  in  Fig.  42  have 
dead  loads  applied  .at  the  joints  as  shown.  Erom  the  fundamental 
equations  for  equilibrium  for  translation,  reaction  R1  =  R2  =  3  W. 

WtanO 
+6  +10  +12  +12  +1O  +G 


Dead  Load  Coefficients 
FIG.  42. 

The  stresses  in  the  members  are  calculated  as  follows:    Resolving 
at  the  left  reaction,  stress  in  i-.r  =  -f-  3  W  sec  0,  and  stress  in  i-y  = 

—  3  W  tan  6.   Resolving  at  first  joint  in  upper  chord,  stress  in  1-2  = 

—  3  W  sec  6 ,  and  stress  in  2-x  =  +  6  W  tan  0  .    Resolving  at  second 
joint  in  lower  chord,  stress  2-3  =  +  2  W  sec0,  and  stress  3-3'  =  — 
8  W  tan#.    And  in  like  manner  the  stresses  in  the  remaining  members 
are  found  as  shown.    The  coefficients  shown  in  Fig.  42  for  the  chords 
are  to  be  multiplied  by  W  tan  0;  while  those  for  the  webs  are  to  be 
multiplied  by  W  seed. 

*Also  called  "Method  of  Sections." 


66 


STRESSES  IN  BRIDGE  TRUSSES 


It  will  be  seen  that  the  coefficients  for  the  web  stresses  are  equal 
to  the  shear  in  the  respective  panels.  Having  found  the  shears  in  the 
different  panels  of  the  truss,  the  remaining  coefficients  may  be  found 
by  resolution.  Pass  a  section  through  any  panel  and  the  algebraic  sum 
of  the  coefficients  will  be  equal  to  zero.  Therefore,  if  two  coefficients 
are  known,  the  third  may  be  found  by  addition. 

Beginning  with  member  i-y,  which  is  known  and  equals  — 3 ; 
coefficient  of  2,-x  =  —  (—    3  —  3)  =  +    6 ; 
coefficient  of  3-y  ==  —  (+    6  +  2)  =  —    8 ; 
coefficient  of  4-*  =  —  (—  8  —  2)  =  +  10 ; 
coefficient  of  5-y  =  —  (+  10  +  i)  =  —  n  ; 
coefficient  of  6-x  =  —  ( —  n  —  i)  =  +  12 ; 
coefficient  of  J-y  =  —  (+12  +  0)  =  —  12  . 
Loading  for  Maximum  Stresses. — The  effect  of  different  positions 
of  the  loads  on  a  Warren  truss  will  now  be  investigated. 

Let  the  truss  in  Fig.  43  be  loaded  with  a  single  load  P  as  shown. 


I* 

•V-  u 

,VJ       <l> 

«<£ 

<o 


Chord  ^5 tresses  -Coefficien As  x  Pfan 
10  3  G  4 

"7  '7  *7  '7 


>r 


FIG.  43. 

The  left  reaction,  R^  =  %P}  and  the  right  reaction,  R2  =  P/?.  The 
stress  in  i-y==  —  %Ptan0,  and  stress  in  i-x  = -\- Q/7  P  sec  0.  The 
stress  in  1-2  =  —  %Psec0  and  stress  in  2-3  =  —  %Psec0,  etc.  The 
remaining  coefficients  are  found  as  in  the  case  of  dead  loads  by  adding 
coefficients  algebraically  and  changing  the  sign  of  the  result. 

In  Fig.  44  the  coefficients  for  a  load  applied  at  each  joint  in  turn 
are  shown  for  the  different  members ;  the  coefficients  for  the  load  on 
left  being  given  in  the  top  line. 


MAXIMUM  AND  MINIMUM  STRESSES. 

Ptan  0 


67 


+/2 

•HO 

•fa 

+  6 

4  4 

4  2 

HO 

42O 

416 

412 

4  a 

44 

4Q 

+16 

iZ4 

4/3 

4/2 

46 

4  6 

412 

fie 

424 

416 

4  a 

+  4 

48 

412 

416 

4ZO 

•no 

4  2 

+  4 

+  6 

4  a 

4IO 

4IZ 

44Z 
7 

+70 

7 

w 

~464 

7 

¥ 

ITz 

7 

111:! 


•it,  -J 

'i 


-  it 

-IS 
-12 


-/a 
-20 

-15 
-IO 

-77 


-21 
-14 


:J 


I        - 

-77  -56 

T  —  T  T 

PtanO 
Maximum  and  Minimum  Coefficients 

FIG.  44. 


if 


The  following  conclusions  may  be  drawn  from  Fig.  44. 

(1)  All  loads  produce  a  compressive  stress  in  the  top  chord  and 
a  tensile  stress  in  the  bottom  chord. 

(2)  All  the  loads  on  one  side  of  a  panel  produce  the  same  kind 
of  stress  in  the  web  members  that  are  inclined  in  the  same  direction  on 
that  side. 

For  maximum  stresses  in  the  chords,  therefore,  the  truss  should 
be  fully  loaded.  For  maximum  stresses  in  the  web  members  the  longer 
segment  into  which  the  panel  divides  the  truss  should  be  fully  loaded; 
while  for  minimum  stresses  in  the  web  members  the  shorter  segment  of 
the  truss  should  be  fully  loaded. 

The  conditions  for  maximum  loading  of  a  truss  with  equal  joint 
loads  are  therefore  seen  to  be  essentially  the  same  as  the  maximum 
loading  of  a  beam  with  a  uniform  live  load. 

Stresses  in  Warren  Truss. — The  coefficients  for  maximum  and 
minimum  stresses  in  a  Warren  truss  due  to  live  load  are  shown  in  Fig.  45. 

These  coefficients  are  seen  to  be  the  algebraic  sum  of  the  coeffi- 
cients for  the  individual  loads  given  in  Fig.  44.  The  live  load  chord 
coefficients  are  the  same  as  for  dead  load,  and  if  found  directly  are 
found  in  the  same  manner. 

The  maximum  web  coefficients  may  be  found  directly  by  taking  off 
one  load  at  a  time  beginning  at  the  left.  The  left  reaction,  which  may 


68 


m 
STRESSES  IN  BRIDGE  TRUSSES. 


be  found  by  algebraic  moments,  will  in  each  case  be  the  coefficient  of 
the  maximum  stress  in  the  panel  to  the  left  of  the  first  load.  A  rule 
for  finding  the  coefficient  of  left  reaction  for  any  loading  is  as  follows: 
Multiply  the  number  of  loads  on  the  truss  by  the  number  of  loads  plus 
unity,  and  divide  the  product  by  twice  the  number  of  panels  in  the  truss 
and  the  result  will  be  the  coefficient  of  the  left  reaction. 


W. 


1     '3      @     '6     ©     -II 

Maximum  in  Webs  P  tan  Q 

Live  Load  Coefficients 
FIG.  45. 


*/ 


-//    C$\    -8 

Minimum,  in  Webs 


If  the  second  differences  of  the  maximum  coefficients  in  the  web 
members  are  calculated,  they  will  be  found  to  be  constant,  which  shows 
that  the  coefficients  are  equal  to  the  ordinates  of  a  parabola. 
Coefficients,  21         15         10         6         3         I 

First  differences,  65  432 

Second  differences,  I  I          I         I 

SECOND  DIFFERENCES  OF  NUMERATORS  OF  WEB  COEFFICIENTS. 
This  relation  gives  an  easy  method  for  checking  up  th^  maximum  web 
coefficients,  since  the  numerators  of  the  coefficients  are  always  the  same 
beginning  with  unity  in  the  first  panel  on  the  right  and  progressing  in 
order  I,  3,  6,  10,  etc.;  the  denominators  always  being  the  number  of 
panels  in  the  truss. 

It  should  be  noted  that  in  the  Warren  truss  the  members  meeting 
on  the  unloaded  chord  always  have  stresses  equal  in  amount,  but  op- 
posite in  sign. 

Stresses  in  Pratt  Truss. —  In  the  Pratt  truss  the  diagonal  member? 
are  tension  members  and  couriers  (see  dotted  members  in  (c)  Fig.  46) 
must  be  supplied  where  there  is  a  reversal  of  stress.  The  coefficients  for 
the  dead  and  live  load  stresses  in  the  Pratt  truss  shown  in  (a)  and  (b) 


STRESSES  IN  PRATT  TRUSS 


Fig.  46,  are  found  in  the  same  manner  as  for  a  Warren  truss.  The 
member  U^  Lt  acts  as  a  hanger  and  carries  only  the  load  at  its  lower 
end.  The  stresses  in  the  chords  are  found  by  multiplying  the  coeffi- 
cients by  W  tan  6,  and  in  the  inclined  webs  by  multiplying  the  co- 
efficients by  W  sec  0.  The  stresses  in  the  posts  are  equal  to  the  ver- 
tical components  of  the  stresses  in  the  inclined  web  members  meeting 
them  on  the  unloaded  chord. 

U! 


L,      -Z|        L2     -4 

U--20-0"--* 

Dead  Load  Coefficients  Dead  Load  Stresses 

Dead  Load  =81bn5  per  Joint.        Sec  6  =  1-28  -  Tan  6  =0-80 

(a) 


Uz  +4j      U3  +57-6     U    +  5I.2 


Live  Load  Coefficients  and  Stresses 
Live  Load=l6Tbns  per  Joint-  Sece  =  l-^ 

(b) 

4-76-8     Uz.  -t-86-4  Us  +Z8-8   Uz  +25-6    L)! 


-48-0    L,   -48-0    Lz  -76-8     L3  -25-6 


Maximum  Stresses  Minimum  Stresses 

(C) 
FIG.  46. 


i  -16-0     L;  -160    |pg 

K     '  *<- 


yo  STRESSES  IN  BRIDGE  TRUSSES 

The  maximum  chord  stresses  shown  on  the  left  of  (c)  are  equal 
to  the  sum  of  the  live  and  dead  load  chord  stresses.  The  minimum 
chord  stresses  shown  on  the  right  of  (c)  are  equal  to  the  dead  load 
chord  stresses. 

The  maximum  and  minimum  web  stresses  are  found  by  adding 
algebraically  the  stresses  in  the  members  due  to  dead  and  live  loads. 

Since  the  diagonal  web  members  in  a  Pratt  truss  can  take  tension 
only,  counters  must  be  supplied  as  Ua  £%  in  panel  L\  Ls.  The  tensile 
stress  in  a  counter  in  a  panel  of  a  Pratt  truss  is  always  equal  to  the 
compressive  stress  that  would  occur  in  the  main  diagonal  web  member 
in  the  panel  if  it  were  possible  for  it  to  take  compression.  Care  must 
always  be  used  to  calculate  the  corresponding  stresses  in  the  vertical 
posts. 

Graphic  Resolution. — The  stresses  in  a  Warren  truss  due  to  dead 
loads  are  calculated  by  graphic  resolution  in  Fig.  47.  The  solution  is 
the  same  as  for  ceiling  loads  in  a  roof  truss.  The  loads  beginning  with 
the  first  load  on  the  left  are  laid  off  from  the  bottom  upwards.  The 
analysis  of  the  solution  is  shown  on  the  stress  diagram  and  truss  and 
needs  no  explanation. 

From  the  stresses  in  the  members  it  is  seen  (a)  that  web  members 
meeting  on  the  unloaded  chord  have  stresses  equal  in  amount  but  op- 
posite in  sign,  and  (b)  that  the  lower  chord  stresses  are  the  arithmetical 
means  of  the  upper  chord  stresses  on  each  side. 

The  live  load  chord  stresses  may  be  obtained  from  the  stress  dia- 
gram in  Fig.  47  by  changing  the  scale  or  by  multiplying  the  dead  load 
stresses  by  a  constant. 

The  live  Joad  web  stresses  may  be  obtained  by  calculating  the  left 
reactions  for  the  loading  that  gives  a  maximum  shear  in  the  panel  (no 
loads  occurring  between  the  panel  and  the  left  reaction),  and  then  con- 
structing the  stress  diagram  up  to  the  member  whose  stress  is  required. 
In  a  truss  with  parallel  chords  it  is  only  necessary  to  calculate  the  stress 
in  the  first  web  member  for  any  given  reaction  since  the  shear  is  con- 
stant between  the  left  reaction  and  the  panel  in  question. 


GRAPHIC  RESOLUTION  71 

The  live  load  web  stresses  may  all  be  obtained  from  a  single  dia- 
gram as  follows:  With  an  assumed  left  reaction  of,  say,  100,000  Ibs. 
construct  a  stress  diagram  on  the  assumption  that  the  truss  is  a  canti- 
lever fixed  at  the  right  abutment  and  that  there  are  no  loads  on  the 


+17.60       +28.10      +3I.GO 


Warren  Truss. 


Dead  Load-700lbs.  per      fffr™     '£5%    ,< 
lineal  M  of  truss  ^> pan  120-0.    /, 


W*  700*20*14000 /bs. 
=  7  fan 5. 


FIG.  47. 

truss.  Then  the  maximum  stress  in  any  web  member  will  be  equal  to 
the  stress  scaled  from  the  diagram,  divided  by  100,000,  multiplied  by 
the  left  reaction  that  produces  the  maximum  stress.  This  method  is  a 
very  convenient  one  for  finding  the  stresses  in  a  truss  with  inclined 
chords. 


72  STRESSES  IN  BRIDGE  TRUSSES 

Algebraic  Moments. — The  dead  and  live  load  stresses  in  a  truss 
with  inclined  chords  are  calculated  by  algebraic  moments  in  Fig.  48. 
The  conditions  for  maximum  loading  are  the  same  in  this  truss  as  in 
a  truss  with  parallel  chords,  and  are  as  follows:  Maximum  chord 
stresses  occur  when  all  loads  are  on;  minimum  chord  stresses  occur 
when  no  live  load  is  on ;  maximum  web  stresses  in  main  members  occur 
when  the  longer  segment  of  the  truss  is  loaded ;  and  minimum  stresses 
in  main  members  and  maximum  stresses  in  counters  occur  when  the 
shorter  segment  of  the  truss  is  loaded.  An  apparent  exception  to  the 
latter  rule  occurs  in  post  U2  L2  which  has  a  maximum  stress  when  the 
truss  is  fully  loaded  with  dead  and  live  loads. 


>. 


V 


M!n  -7.20 

Maximum  and  Minimu 

>" 

Camels  Back  Truss 

by 

Algebraic  Moments 
Dead  Load    5  Ions  per  joint 


FIG.  48. 


To  find  the  stress  in  member  U1  L2  take  moments  about  point  A, 
the  intersection  of  the  upper  and  lower  chords  produced.  The  dead 
load  stress  is  then  given  by  the  equation 

C/!  L2  x  70.7  +  #±  x  60  —  W  x  80  =  o 

E/i  L2  x  70.7  =  —  6  x  60  +  3  x  80  =  —  120  foot-tons 

U^Lz  —  —  i .  70  tons 


ALGEBRAIC  MOMENTS  73 

The  maximum  live  load  stress  occurs  when  all  loads  are  on  except 
Llf  and 

£7±  L2  x  70. 7  +  R!  x  60  =  o 

£/!  L2  x  70. 7  =  —  I  P  x  60  =  —  576  foot-tons 

C7±  L2  =  —  8. 14  tons 

The  maximum  live  load  stress  in  counter  U2  L±  occurs  with  a  load 
at  Llf  and  is  given  by  the  equation 

— U2  LI  x  62.43  +  RI  x  60  —  P  x  80  =  o 

C/2  L!  X  62.43  =  _i    P  X  60  —  8  X  80 

U2  L!  =  —  4.10  tons 

The  dead  load  stress  in  counter  £72  L^  when  main  member  L^  Lz 
is  not  acting  will  be 

U2  L!  x  62.43  =  +  I2°  foot-tons 
t/2  L±  =  +  1.92  tons 

The  maximum  stress  in  U^  L2  is  therefore  —  1.70  —  8. 14  =  — 
9.84  tons,  and  the  minimum  stress  is  zero.  The  maximum  stress  in 
counter  U2  L±  is  +  J-92  —  4.10  =  —  2.18  tons,  and  the  minimum 
stress  is  zero. 

The  stresses  in  the  remaining  members  may  be  found  in  the  same 
manner.  To  obtain  stresses  in  upper  chords  U^  U2  and  U2  U2,  take  mo- 
ments about  L2  as  a  center ;  to  obtain  stress  in  lower  chord  Lb  L±  take 
moments  about  U^  as  a  center.  The  dead  load  and  maximum  live  load 
stress  in  post  U2  L2  is  equal  to  the  vertical  component  of  the  dead  and 
live  loads,  respectively,  in  upper  chord  t/±  U2.  The  stresses  in  L0  Ulf 
L0  LI,  L2  Z/2,  U2  C712  and  U2  L12  are  most  easily  found  by  algebraic 
resolution. 

Graphic  Moments. — The  dead  load  stresses  in  the  chords  of  a 
Warren  truss  are  calculated  by  graphic  moments  in  Fig.  49. 

Bending  Moment  Polygon. — The  upper  chord  stresses  are  given 
by  the  ordinates  to  the  bending  moment  parabola  direct,  while  the 
lower  chord  stresses  are  arithmetical  means  of  the  upper  chord  stresses 


74 


STRESSES  IN  BRIDGE  TRUSSES 


on  each  side,  and  are  given  by  the  ordinates  to  the  chords  of  the  parabola 
as  shown  in  Fig.  49. 

The  parabola  is  constructed  as  follows:  The  mid-ordinate,  47,  is 
made  equal  to  the  bending  moment  at  the  center  of  the  truss  divided  by 
the  depth ;  in  this  case  the  mid-ordinate  is  the  stress  in  6-x;  if  the  num- 


FIG.  49. 

ber  of  panels  in  the  truss  were  odd  the  mid-ordinate  would  not  be  equal 
to  any  chord  stress.  The  parabola  is  then  constructed  as  shown  in  Fig. 
49.  The  live  load  chord  stresses  may  be  found  from  Fig.  49  by  chang- 
ing the  scale  or  by  multiplying  the  dead  load  chord  stresses  by  a  con- 
stant. 

Shear  Polygon. — In  Chapter  IX  it  was  shown  that  the  maximum 
shear  in  a  beam  at  any  point  could  be  represented  by  the  ordinate  to  a 
parabola  at  any  point.  The  same  principle  holds  for  a  bridge  truss 
loaded  with  equal  joint  loads,  as  will  now  be  proved. 

In  Fig.  50  assume  that  the  simple  Warren  truss  is  fixed  at  the  left 
end  as  shown,  and  that  right  reaction  R:  is  not  acting.  Then  with  all 
joints  fully  loaded  with  a  live  load  Pf  construct  a  force  polygon  as 
shown,  with  pole  o  and  pole  distance  H  —  span  L,,  and  beginning  at 
point  a  in  the  load  line  of  the  force  polygon  construct  the  equilibrium 
polygon  a  g  h  for  the  cantilever  truss. 

Now  the  bending  moment  at  the  left  support  will  be  equal  to 


GRAPHIC  MOMENTS 
X 


75 


© 
-* — 7-* 

/  \    2  /  \    4  /\    6  /  \   4'  /  \  2'  /  \ 

' *>'''' 


FIG.  50. 

ordinate  F!  multiplied  by  the  pole  distance  H.  But  the  truss  is  a  sim- 
ple truss  and  the  moment  of  the  right  reaction  will  be  equal  to  the 
moment  at  the  left  abutment  and 

Y1  H  =  Rt  L 
and  since  H  =  L 

YL  =  RL  and 


Now,  with  the  loads  remaining  stationary,  move  the  truss  one  panel  to 
the  right  as  shown  by  the  dotted  truss.  With  the  same  force  polygon 
draw  a  new  equilibrium  polygon  as  above.  This  equilibrium  polygon 
will  be  identical  with  a  part  of  the  first  equilibrium  polygon  as  shown. 
As  above,  the  betiding  moment  at  left  reaction  is  Y3  H  =  Y3  L  = 
Rz  L,  and  Yz  =  R3.  In  like  manner  F5  can  be  shown  to  be  the  right 
reaction  with  three  loads  on,  etc.  Since  the  bridge  is  symmetrical  with 
reference  to  the  center  line,  the  ordinates  to  the  shear  polygon  in  Fig.  50, 
are  equal  to  the  maximum  shears  in  the  panel  to  the  right  of  the  or- 
dinate as  the  load  moves  off  the  bridge  to  the  right. 


7 6  STRESSES  IN  BRIDGE  TRUSSES 

To  draw  the  shear  parabola  direct,  without  the  use  of  the  force 
and  equilibrium  polygons  proceed  as  follows :  At  a  distance  of  a  panel 
length  to  the  left  of  the  left  abutment  lay  off  to  scale  a  load  line  equal 
to  one-half  the  total  load  on  the  truss,  divide  this  load  line  into  as  many 
parts  as  there  are  panels  in  the  truss,  and  beginning  at  the  top,  which 
call  I,  number  the  points  of  division  of  the  load  line  I,  2,  3,  etc.,  as  in 
Fig.  49.  Drop  vertical  lines  from  the  panel  points  and  number  them 
i,  2,  3,  etc.,  beginning  with  the  load  line,  which  will  be  numbered  I, 
the  left  reaction  numbered  2,  etc.  Now  connect  the  numbered  points  in 
the  load  line  with  the  point  f,  which  is  under  the  first  panel  to  the  left 
of  the  right  abutment;  and  the  intersection  of  like  numbered  lines  will 
give  points  on  the  shear  parabola.  It  should  be  noted  that  the  line  h  g 
is  a  secant  to  the  parabola  and  not  a  tangent  as  might  be  expected. 

The  dead  load  shear  is  laid  off  positive  downward  in  Fig.  50  to  the 
same  scale  as  the  live  load  shears,  and  the  maximum  and  minimum 
shears  due  to  dead  and  live  loads  are  added  graphically.  The  stresses 
in  the  web  members  are  calculated  graphically  in  Fig.  50. 

Wheel  Loads. — The  criteria  for  maximum  moments  and  shears 
in  bridge  trusses  loaded  with  wheel  loads  are  as  follows : 

(1)  Maximum  Moment  at  any  joint  in  a  bridge  loaded  with 
wheel  loads  will  occur  when  the  average  load  on  the  left  of  the  section 
is  the  same  as  the  average  load  on  the  whole  span. 

(2)  Maximum  Shear  in  any  panel  in  a  bridge  loaded  with  wheel 
loads  will  occur  when  the  load  on  the  panel  is  equal  to  the  load  on  the 
bridge  divided  by  the  number  of  panels. 

These  criteria  will  be  proved  by  means  of  the  influence  diagram 
in  the  following  discussion. 

For  a  more  complete  discussion  of  the  subject  see  standard  books 
on  bridge  design.  For  the  calculation  of  stresses  in  simple  trusses  see 
problems  in  Appendix  II. 


INFLUENCE  DIAGRAMS 


77 


INFLUENCE  DIAGRAMS.— An  influence  diagram  (commonly 
called  an  influence  line)  shows  the  variation  of  the  effect  of  a  moving 
load  or  a  system  of  loads  on  a  beam  or  truss.  The  difference  between 
bending  moment  or  shear  diagrams  and  influence  diagrams  is  that  the 
bending  moment  and  the  shear  diagram  gives  the  moment  and  shear, 
respectively,  at  any  point  for  a  fixed  system  of  loads,  while  an  in- 
fluence diagram  gives  the  moment  or  shear,  etc.,  at  a  fixed  point  for 
a  moving  system  of  loads.  Influence  diagrams  are  used  principally 
for  finding  the  position  of  moving  loads  that  will  produce  maximurn 
shears,  moments,  reactions,  or  stresses,  although  they  may  be  used 
for  calculating  the  quantities  themselves.  For  convenience  where  a 
number  of  loads  are  considered  the  influence  diagrams  are  drawn  for 
a  single  unit  load.  The  unit  influence  diagram  may  then  be  used  for 
any  load  by  multiplying  by  the  given  load.  The  unit  influence  diagram 
will  be  referred  to  in  the  following  discussion. 

Maximum  Moment  in  a  Truss  or  Beam. — Let  P±  in  Fig.  5oa, 
represent  the  summation  of  the  moving  loads  to  the  left  of  the  panel 
point  2'  and  P2  be  the  summation  of  the  moving  loads  to  the  right. 


u-  a  -^ XL-a 


a,  -J    ^-dx  4  --dx        ^az         5 

FIG.  5oa.     INFLUENCE  DIAGRAM  FOR  MOMENTS. 

The  influence  diagram  for  the  point  2'  is  constructed  by  calculating 

a(L  —  a) 
the  bending  moment  at  2'  due  to  a  unit  load,  =  —  —  ==  ordinate 


7$  STRESSES  IN  BRIDGE  TRUSSES 

2-4,  and  drawing  lines  1-2  and  2-3.    The  equation  of  the  line  1-2  is 

*(L  —  a) 
y=—L  — 
and  the  equation  of  the  line  2-3  is 

a(L-X) 


Now  when  x=a  the  two  lines  have  a  common  ordinate  which  is  equal  to 

a(L  —  a) 

-   -  .     Also  when  x  =  L  the  ordinate  to   1-2  =  L  —  a  ;  while 

JL» 

when  x  =  o,  the  ordinate  to  2-3  is  a,  as  is  seen  in  Fig.  5oa.  This  rela- 
tion gives  an  easy  method  of  constructing  an  influence  diagram  for 
moments  for  any  point  in  a  beam  or  truss. 

Now  in  Fig.  5oa  the  bending  moment  at  2'  due  to  the  loads  P^  and 


P2is 


(a) 


Now  move  the  loads  P±  and  P2  a  short  distance  to  the  left,  the  dis- 
tance being  assumed  so  small  that  the  distribution  of  the  loads  will 
not  be  changed,  and 


M  +  dM  =  P1  (3<1-</3'1)  +P*  (yz  +  dy2)  fb) 

Subtracting  (a)  from  (b)  and  placing  d  M  =  o,  we  have 


But  d  yI  =  d  x  tan  04  =  d  x  -  ,  and  d  y2  =  d  x  tan  a2  =  d  x-,  and 

•L'  A. 


from  which  P^  a  —  P1  L  +  P2a  =  o,  and  (Pi 


INFLUENCE  DIAGRAMS  79 

Solving,  we  have 


From  (c)  it  follows  that  the  maximum  bending  moment  at  2  occurs 
zvhen  the  average  load  on  the  left  of  the  section  is  the  same  as  the 
average  load  on  the  entire  bridge. 

Uniform  Loads.  —  In  Fig.  5oa,  the  bending  moment  at  2'  due  to  a 
uniform  load  p  d  x  will  be  p  y  d  x  in  (a).  But  y  d  x  is  the  area  of  the 
influence  diagram  under  the  uniform  load,  and  the  bending  moment 
at  2'  due  to  a  uniform  load  will  be  equal  to  the  area  of  the  influence 
diagram  covered  by  the  load,  multiplied  by  the  load  per  unit  of  length. 
For  a  uniform  load,  p,  covering  the  entire  span  the  bending  moment 
at  2'  will  be  p  times  the  area  of  the  influence  diagram  1-2-3.  For  a 
uniform  load  the  bridge  must  be  fully  loaded  to  obtain  maximum  bend- 
ing moment  at  any  point.  It  will  be  seen  that  the  general  criterion  for 
maximum  moment  is  satisfied  when  the  bridge  is  fully  loaded  with  a 
uniform  load. 

Maximum  Shear  in  a  Truss.  —  Let  Plf  P2,  and  P3  in  Fig.  5ob 
represent  the  loads  on  the  left  of  the  panel,  on  the  panel,  and  on  the 
right  of  the  (m  +  i)st.  panel,  respectively.  It  is  required  to  find  the 
position  of  the  loads  for  a  maximum  shear  in  the  panel. 

ffl 

With  a  load  unity  at  2'  the  shear  in  the  panel  is  --  ,  and  1-2  is  the 

n 

influence  shear  line  for  loads  to  the  left  of  the  panel.    With  a  load  unity 

n  —  m  —  i 

at   3'   the    shear    in   the   panel   is   -  -  ,    and    3-4   is   the    in- 

n 

fluence  shear  line  for  loads  to  the  right  of  the  panel.     For  a  load  on 

m  n  —  m  —  I 

the  panel  the  shear  will  vary  from  —  —   at  2'  to    -       -    at  3', 

n  n 

and  the  line  2-3  is  the  influence  shear  line  for  loads  on  the  panel. 

The  influence  diagram  for  the  entire  span  is  the  polygon  1-2-3-4. 
It  will  be  seen  that  the  lines  1—2  and  3-4  are  parallel,  and  are  at  a 
distance  unity  apart. 

The  total  shear  in  the  panel  will  then  be 

S=—P*yi  +  P*y*  +  P*y.  (d) 


8o 


STRESSES  IN  BRIDGE  TRUSSES 


Now  move  the  loads  a  short  distance  to  the  left,  the  distance  being 
assumed  so  small  that  the  distribution  of  the  loads  will  not  be  changed, 
and 

S  +  dS  =  —  P1(y1  —  dyi)+P2(y2  —  d  y2)  +  Ps  (ys  + d  y3)  (e) 
Subtracting  (d)  from  (e)  and  solving  for  a  maximum 


But 


d  yt  =  d  x  tan  a±  =  d  x 
d  y2  =  d  x  tan  a2  =  d  x 


nl 

n —  I 
nl 


=  dx  tan  a3  =  dx  — 
nl 


FIG.  5ob.    INFLUENCE  DIAGRAM  FOR  SHEAR. 
and  substituting  we  have 


nl 


nl 


and 
and 


INFLUENCE  DIAGRAMS  Si 


P  + 
Pz=    l^  (f) 


From  (f)  it  follows  that  the  maximum  shear  in  the  panel  will  occur 
when  the  load  on  the  panel  is  equal  to  the  load  on  the  bridge  divided 
by  the  number  of  panels  in  the  bridge. 

Uniform  Loads.  —  From  Fig.  5ob,  it  will  be  seen  that  for  a  uni- 
form load  the  maximum  shear  in  the  panel  will  occur  when  the  uniform 
load  extends  from  the  right  abutment  to  that  point  in  the  panel  where 
the  line  2-3  passes  through  the  line  1-4  (where  the  shear  changes  sign). 
For  a  minimum  shear  in  the  panel  (maximum  shear  of  the  opposite 
sign)  the  load  should  extend  from  the  left  abutment  to  the  point  in 
the  panel  where  the  shear  changes  sign.  For  equal  joint  loads,  load 
the  longer  segment  for  a  maximum  shear  in  the  panel,  and  load  the 
shorter  segment  for  a  minimum  shear  in  the  panel. 

Maximum  Floor  Beam  Reaction.  —  It  is  required  to  find  the 
maximum  load  on  the  floor  beam  at  2'  in  (a)  Fig.  500  for  the  loads 
carried  by  the  floor  stringers  in  the  panels  i'—  2'  and  2'—  3'. 

In  (a)  the  diagram  1-2-3  1S  the  influence  diagram  for  the  shears 
at  2'  due  to  a  load  unity  at  any  point  in  either  panel.  In  (b)  the  dia- 
gram 1-2-3  i§  tne  influence  diagram  for  bending  moment  at  2'  for  a 
unit  load  at  any  point  in  the  beam.  Now  diagram  in  (a)  differs  from 
diagram  in  (b)  only  in  the  value  of  the  ordinate  2-4.  It  will  be  seen 
that  the  reaction  at  2'  in  (a)  may  be  obtained  from  the  diagram 
in  (b)  for  any  system  of  loads  if  the  ordinates  are  multiplied  by 

^1   +  ^2 

-  .  We    can    therefore    use    diagram     (b)     for    obtaining    the 


maximum  floor  beam  reaction  if  we  multiply  all  ordinates  by 


To  obtain  the  maximum  floor  beam  reaction,  therefore,  take  a 
simple  beam  equal  to  the  sum  of  the  two  panel  lengths,  and  find  the 
maximum  bending  moment  at  a  point  in  the  beam  corresponding  to 

d,  +  d2 

the  panel  point.    This  maximum  moment  multiplied  by  -    will  be 

d^d2 

the  maximum  floor  beam  reaction.     If  the  two  panels  are  equal  in 


83  STRESSES  IN  BRIDGE  TRUSSES 

length  the  maximum  bending  moment  at  the  center  of  the  beam  multi- 

2 

plied  by     -,  where  d  is  the  panel  length,  will  give  the  maximum  floor 
d 

beam  reaction. 


-TT 

'»  '  L-_v 

(a)  '  tb) 

FIG.  500.    INFLUENCE  DIAGRAM  FOR  MAXIMUM  FLOOR  BEAM 

REACTION. 

Maximum  Moment  in  the  Unloaded  Chord  of  a  Through  Warren 
Truss. — Let  P±  in  Fig.  5od  represent  the  summation  of  the  moving 
loads  on  the  left  of  the  panel  4'~5',  P2  represent  the  summation  of  the 

1*. „ -J 


_g 

?U- L- 


. 

FIG.  5od.     INFLUENCE  DIAGRAM  FOR  MOMENTS  IN  THE  UNLOADED 
CHORD  OF  A  THROUGH  WARREN  TRUSS. 

moving  loads  on  the  panel,  and  P3  represent  the  summation  of  the 
moving  loads  to  the  right  of  the  panel.  The  influence  diagram  for  the 
point  2  is  the  diagram  1-4-5-3,  tne  n'nes  I~4  and  5-3  are  the  same  as  for 


MAXIMUM  STRESSES  IN  A  BRIDGE  WITH  INCLINED  CHORDS.  82a 

a  point  on  the  loaded  chord,  while  the  influence  line  for  the  panel  4'~5' 
is  the  line  4-5. 

Xow  the  bending  moment  at  2  due  to  the  three  loads  is 

M  =  P1.y1  +  P2-y2  +  Ps-y3  (g) 

Xow  move  the  loads  Pit  P2,  P3  a  short  distance  to  the  left,  the  dis- 
tance being  assumed  so  small  that  the  distribution  of  the  loads  will  not 
be  changed,  and 


=P1(yl  —  dy1)  +  P,(yt-dyt)  +P,(yt  +  dyt)      (h) 

Subtracting  (g)  from  (h),  and  solving  for  a  maximum 

dM  =  —  P1'dy1  —  P2'dy2  +  P9'dys  =  o  (i) 

Xow  d\\  =  d.Y-tana1,  dy2  =  d.Y'taiia2,  and  dys  =  Jj 


tana1  =  (L  —  a)/L,  ta.na3  =  a/L,  and  tana., 

__  [L  —  (a  —  &  +  /)]  tana3  —  (a  —  b)  tanat 


and  tana2  =  (L-b  —  a- 

Substituting  the  values  of  tanax,  tana2  and  tana3  in  (i)  we  have 

—  Pi(L  —  a)/L  —  P2(L-b  —  a-l)/L.l  +  P3.a/L  =  o 
Solving  and  placing  P  =  P1-\-P2-}-  P3,  we  have 

P/L=(Pl.l  +  Pt.b)/a-l  (j) 

Equation  (j)  is  the  criterion  required. 

Maximum  Stresses  in  a  Bridge  with  Inclined  Chords.  —  Let  U24* 
be  a  web  member  in  a  truss  with  inclined  chords  in  Fig.  506.  Point  A 
is  the  intersection  of  the  upper  chord  U-JJ2  and  the  lower  chord  2'4'. 
The  stress  in  U24f  equals  the  moment  of  the  external  forces  about  the 
point  A,  divided  by  the  arm  c.  The  stress  in  the  web  member  C724'  will 
then  be  a  maximum  when  the  bending  moment  at  A  is  a  maximum. 
To  draw  the  moment  influence  diagram  for  the  point  A,  calculate  the 
bending  moments  about  A  for  the  unit  loads  at  2'  and  4'.  With  a  load 
unity  at  4'  the  moment  at  A  is  (L  —  a  —  l)e/L,  and  with  a  load  unity 
at  27  the  moment  at  A  is  (L  —  a)e/L  —  (fl  +  tf),  a  negative  quantity. 


82b 


STRESSES  IN  BRIDGE  TRUSSES. 


Laying  off  4-6  and  2-7  equal  to  these  moments,  respectively,  the  influ- 
ence diagram  for  bending  moment  at  A  is  the  polygon  1-2-4-5. 


FIG.  5oe. 

The  maximum  stress  in  U24'  occurs  when  some  of  the  wheels  at 
the  heat"  of  the  train  are  in  the  panel  2'4',  and  in  unusual  cases  only, 
when  a  load  is  to  the  left  of  2'.  Load  P2  representing  the  summation 
of  the  loads  to  the  left  of  4'  will  always  come  in  the  panel  2'4'.  Load 
P3,  representing  the  summation  of  the  loads  to  the  right  of  the  panel, 
will  always  come  to  the  right  of  the  panel  2'4'«  Now  the  moment 
at  A  is 

M  =  P2-y2  +  P3'y3  (k) 

Now  move  the  loads  a  differential  distance  to  the  left,  it  being  assumed 
that  the  distribution  of  the  loads  is  not  changed,  and 

Pz(y2  —  dy2)  +Ps(ys  +  dy&)  (1) 


Subtracting  (k)  from  (1),  and  solving  for  a  maximum  we  have 


(m) 


Now  dy2  =  dj:'tana.2,  and  dy5  — 


,  and 


RESOLUTION  OF  THE  SHEAR. 


82C 


P2-tan  a2  +  F3-tan  a3  =  o 


and  if  P  = 


(n) 

(o) 


Now  tan  a2  =  —  ( / •  e/L  —  a  —  e)/l,  and  tan  a3  =  e/L,  and  substituting 
in  (n)  we  have 

P/L  =  P,(i +«/*)//  (P) 

Now  for  a  uniform  load  the  maximum  stress  in  the  member  t/24' 
will  occur  when  the  truss  is  loaded  from  the  right  abutment  to  the  point 
3',  while  the  minimum  stress  will  occur  when  the  load  extends  from 
the  left  abutment  to  the  point  3'.  The  critical  point  3  can  be  calcu- 
lated by  drawing  the  lines  M-2r-^f  and  N-4'-$'.  For  wheel  loads  no 
load,  should  in  general,  pass  3'  from  the  right  to  give  a  maximum 
stress  in  the  member. 

By  substituting  e  =  oo  in  (p)  we  have  the  criterion  for  maximum 
shear  in  a  panel  of  a  bridge  with  parallel  chords. 

Resolution  of  the  Shear. — In  Fig.  5of  the  stresses  U,  D  and  L 
hold  in  equilibrium  the  external  forces  on  the  left  of  the  section  cutting 
these  members.  These  external  forces  consist  of  a  left  reaction,  R,  at 


<5     R, 


the  left  abutment  and  a  force  at  2,  equal  to  the  reaction  of  the  stringer 
2-3.  The  resultant,  S,  of  these  two  forces  acts  at  a  point  a  little  to 
the  left  of  the  left  reaction.  Its  position  may  be  determined  by  mo- 
ments. Referring  to  Fig.  5of,  let  the  resultant,  S,  be  replaced  by  the 
two  forces  P±  and  P3,  P±  acting  upwards  at  I  and  P3  acting  downward 
at  3  as  shown.  Now  taking  moments  about  point  i,  and 


82d  STRESSES    IN    BRIDGE    TRUSSES 

S-a  =  P..l  (q) 

Now  the  bending  moment  at  I  equals  Mlt  and 

Pa=,S-a/l  =  MJl  (r) 

Similarly  by  taking  moments  at  3,  we  have 

S(a  +  l)==P1-lf  but  S(a  +  /)=M8,  and  Pi  =  M3/l 
Now 

S  =  P1  —  P,  =  Mi/l  —  Ms/l  (s) 

where  £  is  the  shear  in  the  panel. 


CHAPTER  XL 
STRESSES  IN  A  TRANSVERSE  BENT. 

Dead  and  Snow  Load  Stresses. — The  stresses  due  to  the  dead 
load  in  the  trusses  of  a  transverse  bent  are  the  same  as  if  the  trusses 
were  supported  on  solid  walls.  The  stresses  in  the  supporting  columns 
are  due  to  the  dead  load  of  the  roof  and  the  part  of  the  side  walls 
supported  by  the  columns,  and  are  direct  compressive  stresses  if  the 
columns  are  not  fixed  at  the  top.  If  the  columns  are  fixed  at  the  top 
the  deflection  of  the  truss  will  cause  bending  stress  in  the  columns. 
The  dead  load  produces  no  stress  in  the  knee  braces  of  a  bent  of  the 
type  shown  in  Fig.  I  except  that  due  to  deflection  of  the  truss,  which 
may  usually  be  omitted  The  stresses  may  be  computed  by  algebraic 
or  graphic  methods. 

The  stresses  due  to  snow  load  are  found  in  the  same  way  as  the 
dead  load  stresses.  In  localities  having  a  heavy  fall  of  snow  the  freez- 
ing and  thawing  often  cause  icicles  to  form  on  the  eaves  of  sufficient 
weight  to  tear  off  the  cornice,  unless  particular  care  has  been  exercised 
in  the  design  of  this  detail. 

Wind  Load  Stresses. — The  analysis  of  the  stresses  in  a  bent  due 
to  wind  loads  is  similar  to  the  analysis  of  the  stresses  in  the  portal  of  a 
bridge.  The  external  wind  force  is  taken  (i)  as  horizontal  or  (2) 
as  normal  to  all  surfaces.  The  first  is  the  more  common  assumption, 
although  the  second  is  more  nearly  correct.  For  a  comparison  of  the 
stresses  in  a  bent  due  to  the  wind  acting  horizontal  and  normal,  see 
Figs.  54,  55,  56  and  57,  and  Table  V.  In  the  discussion  which  immed- 
iately follows,  the  wind  force  will  be  assumed  to  act  horizontally. 

The  magnitude  of  the  wind  stresses  in  the  trusses,  knee  braces  and 


84  STRESSES  IN  A  TRANSVERSE  BENT 

columns  will  depend  (a)  upon  whether  the  bases  of  the  columns  are 
fixed  or  free  to  turn,  (b)  upon  whether  the  columns  are  rigidly  fixed 
to  the  truss  at  the  top,  and  (c)  upon  the  knee  brace  and  truss  con- 
nections. Of  the  numerous  assumptions  that  might  be  made,  only  two, 
the  most  probable,  will  be  considered,  viz.:  (I)  columns  pin  connected 
(free  to  turn)  at  the  base  and  top,  and  (II)  columns  fixed  at  the  base 
and  pin  connected  at  the  top. 

Columns  in  mill  buildings  are  usually  fixed  by  means  of  heavy 
bases  and  anchor  bolts.  Where  the  columns  support  heavy  loads  the 
dead  load  stress  in  the  columns  will  assist  somewhat  in  fixing  them. 
Where  the  dead  load  stress  plus  algebraically  the  vertical  component 
of  the  wind  stress  in  the  column,  multiplied  by  one-half  the  width  of 
the  base  of  the  column  parallel  to  the  direction  of  the  wind,  is  greater 
than  the  bending  moment  developed  at  the  base  of  the  leeward 
column  when  the  columns  are  considered  as  fixed,  the  columns  will  be 
fixed  without  anchor  bolts  (see  Chapter  XII,  Fig.  61).  In  any  case 
the  resultant  moment  is  all  that  will  be  taken  by  the  anchor  bolts.  The 
dead  load  stresses  in  mill  buildings  are  seldom  sufficient  to  give  material 
assistance  in  fixing  the  columns.  Unless  care  is  used  in  anchoring 
columns  it  is  best  to  design  mill  buildings  for  columns  hinged  at  the 
base. 

The  general  problem  of  stresses  in  a  transverse  bent  for  Case  I 
and  Case  II,  in  which  the  stresses  and  forces  are  determined  by  alge- 
braic methods,  will  now  be  considered.  The  application  of  the  general 
problem  will  be  further  explained  by  the  graphic  solution  of  a  par- 
ticular problem. 

ALGEBRAIC    CALCULATION    OF    STRESSES:     Case  I. 

Columns  Free  to  Turn  at  Base  and  Top.— In  Fig.   51,  H  =  Hl 
W 

-  2    —  horizontal  reaction  at  the  base  of  the  column  due  to  external 

wind  force,  W. 

W I 
V  =  —  V1  =  ~^j-  =  vertical  reaction  at  base  of  column  due  to 

the  wind  force,  W. 

The  wind  produces  bending  in  the  columns,  and  also  the  direct 


COLUMNS  HINGED  AT  THE  BASE  85 

stresses  F  and  F1.  Maximum  bending  occurs  at  the  foot  of  the  knee 
brace  and  is  equal  to  (H  —  W-^)  d  on  the  \vindward  side,  and  H1  d 
on  the  leeward  side.  These  bending  moments  are  the  same  as  the  bend- 
ing moments  in  a  simple  beam  supported  at  both  ends  and  loaded  with 
a  concentrated  load  at  the  point  of  maximum  moment.  Since  the  max- 


H'         "  >•' 

v'(b)         (c) 
Leeward  Col-     Beam 


H1 

(d)  (e) 

Shear         Moment 


FIG.  51. 


imum  moment  occurs  at  the  foot  of  the  knee  brace  in  the  leeward 
column,  we  will  consider  only  that  side.  We  will  assume  that  the  lee- 
ward column  (b),  Fig.  51,  acts  as  a  simple  beam  with  reactions  H1  and 
C  and  a  concentrated  load  B,  as  in  (c).  The  reaction  C  and  load  B  will 
now  be  calculated. 

From  the  fundamental  equation  of  equilibrium,  summation  hori- 
zontal forces  equal  zero,  we  have 

B  =  H-  +  C  (25) 

Taking  moments  about  b,  we  have 

C  (h  —  d)=Hld 

c=  H1  d  (26) 

h  —  d 

The  stresses  K,  U  and  L  can  be  computed  by  means  of  the  follow- 
ing formulas: 

K  =  B  cosecant  m  (27) 

where  m  =  angle  knee  brace  makes  with  column; 

U  =   (F1  —  K  cos  m)  cosecant  n  (28) 

where  n  =  angle  of  pitch  of  roof;  and 


S6  STRESSES  IN  A  TRANSVERSE  BENT 

L  =  C  —  U  cos  n  (29) 

In  calculating  the  corresponding  stresses  on  the  windward  side, 
the  wind  components  acting  at  the  points  (a),  (b)  and  (c)  must  be 
subtracted  from  H,  B  and  C. 

The  shear  in  the  leeward  column  is  equal  to  H1  below  and  C  above 
the  foot  of  the  knee  brace,  (d)  Fig.  51. 

The  moment  in  the  column  is  shown  in  (e),  Fig.  51,  and  is  a  max- 
imum at  the  foot  of  the  knee  brace  and  is,  M  =  H1  d. 

The  maximum  fibre  stress  due  to  wind  moment  and  direct  loading 
in  the  columns  will  occur  at  the  foot  of  the  knee  brace  in  the  leeward 
column,  and  will  be  compression  on  the  inside  and  tension  on  the  out- 
side fibres,  and  is  given  by  the  formula* 

(30) 

where  f1  =  maximum  fibre  stress  due  to  flexure ; 
/2  =  fibre  stress  due  to  direct  load  P; 
A  =  area  of  cross-section  of  column  in  square  inches; 
M  =  bending  moment  in  inch-pounds  =  H1  d; 
y  =  distance  from  neutral  axis  to  extreme  fibre  of  column  in 

inches ; 
I  =  Moment  of  Inertia  of  column  about  an  axis  at  right  angles 

to  the  direction  of  the  wind ; 

P  =  direct  compression  in  the  column  in  pounds ; 
h  =  length  of  the  column  in  inches ; 

£  =  the  modulus  of  elasticity  of  steel  =  28,000,000 ; 

P  h2 

IQ  £  is  minus  when  P  is  compression  and  plus  when  P  is  tension. 

The  maximum  compressive  wind  stress  is  added  to  the  direct  dead 
and  minimum  snow  load  compression  and  governs  the  design  of  the 
column. 


"This  formula  was  first  deduced  by  Prof.  J.  B.  Johnson.  For  deduction 
of  the  formula  see  Chapter  XV,  of  "Modern  Framed  Structures"  by  Johnson, 
Bryan  and  Turneaure. 


COLUMNS  FIXED  AT  THE  BASE 


87 


Having  the  stresses  K,  U ,  and  L,  the  remaining  stresses  in  the 
truss  can  be  obtained  by  ordinary  algebraic  or  graphic  methods. 

For  a  simple  graphic  solution  of  the  stresses  in  a  bent  for  Case  I, 
in  which  these  stresses  are  computed  graphically,  see  Fig.  54  for  wind 
horizontal,  and  Fig.  56  for  wind  normal  to  all  surfaces. 

Case  II.  Columns  Fixed  at  the  Base. — With  columns  fixed 
at  the  base  the  columns  may  be  (i)  hinged  at  the  top,  or  (2)  rigidly 
fixed  to  the  truss. 

(i)  Columns  fixed  at  the  base  and  hinged  at  the  top. — It  will  be 
further  assumed  that  the  deflections  at  the  foot  of  the  knee  brace  and 
the  top  of  the  column,  Fig.  52,  are  equal. 


(a) 

External  Forces 


1C) 
Leeward  CoL    Beam 

FIG.  52. 


H 
(d)         (e) 

5hear     Moment 


In  Fig.  52  we  have  as  in  Case  I 


V  and  F1  are  not  as  easily  found  as  in  Case  I,  but  will  be  cal- 
culated presently. 

The  leeward  column  will  be  considered  and  will  have  horizontal 
external  forces  acting  on  it  as  shown  in  (c)  Fig.  52.  For  convenience 
we  will  consider  the  leeward  column  as  a  beam  fixed  at  a  and  acted 
upon  by  the  horizontal  forces  B  and  C  as  shown  in  (c)  Fig.  52,  the  de- 
flection of  the  points  b  and  c  being  equal  by  hypothesis. 

From  the  fundamental  condition  of  equilibrium,  summation  hori- 
zontal forces  equal  zero,  we  have 

B  =  H1  +  C  (31) 


STRESSES  IN  A  TRANSVERSE:  BENT 

To  obtain  B  and  C  a  second  equation  is  necessary. 

From  the  theory  of  flexure  we  have  for  the  bending  moment  in 
the  column  at  any  point  yf  where  the  origin  is  taken  at  the  base  of  the 
column,  when  y  =  d 


=  B(d-y)-  C(h  -y)  (32) 


Integrating  (32)  between  the  limits  y  =  o  and  y  =  d,  we  have 


Now  (33)  equals  £  /  times  the  angular  change  in  the  direction  of  the 
neutral  axis  of  the  column  from  y  =  o  to  y  =  d. 
When  y  *>  d,  we  have 

jO  (34) 


Integrating  (34)  we  have 

Fi  (35) 


(35)  equals  H  I  times  the  change  in  direction  of  the  neutral 
axis  of  the  column  at  any  point  from  y  =  d  to  y  =  h. 

To  determine  the  constant  F2  in  (35)  we  have  the  condition  that 
the  angle  at  y  =  d  must  be  the  same  whether  determined  from  equation 
(33)  or  equation  (35).  Equating  (33)  and  (35)  and  making  y  =  d, 
we  have 

K-2f  (36) 

Substituting  this  value  of  Fz  in  (35)  we  have 

*'%—C*,+  ££+*f  (37) 

Integrating  (37)  between  the  limits  y  =  d  and  y  =  h,  we  have 


(38) 


COLUMNS  FIXED  AT  THE  BASE  89 

Now   (38)   equals  H  I  times  the  deflection  of  the  column  from 
y  =  d  to  y  =  h,  which  equals  zero  by  hypothesis. 
Solving  (38)  we  have 

C  3d2  A  —  3d3 


B  "'    —  3  h  d2  -. 

_  3flr2 (39) 

~   2h2  +2dh-  d2 

In  a  beam  fixed  at  one  end  there  is  a  point  of  inflection  at  some 
point,  between  y  =  o  and  3;  =  d,  where  the  bending  moment  equals 
zero.  Now  if  y0  equals  the  value  of  y  for  the  point  of  inflection,  we 
have  from  (32) 

B  (d  —  v0)  =  C  (h  —  j0)  and 

CB  =  TT^T  (40) 

r>  H  — _>'o 

Equating  the  second  members  of  equations  (39)  and  (40)  and 
solving  for  y0,  we  have 


To  find  the  relations  between  y0  and  dt  we  will  substitute  h  in 
terms  of  d  in  (41)  and  solve  for  y0. 

For       d=~,  y»  =  Sd 

*  =  \*.       y«  =  \* 

d=h,  yQ  =  ±d 

2 

Solving  (31)  and  (39)  foi  C,  we  have 

C=       ^l 3  ^2 .  (A1\ 

2      (h  —  d)(h+2d) 

To  find  the  moment  M^  at  the  base  of  the  leeward  column,  we 
have  from  (32) 

Af  K  —  B  d  —  C  h 


90  STRESSES  IN  A  TRANSVERSE  BENT 

Substituting  the  value  of  B  given  in  (31)  we  have 


Eliminating  h  and  d  by  means  of  (41)  and  (42)  we  have  finally 
to\  =  H1  y0  (43) 

In  like  manner  it  can  be  shown  that  the  moment  at  the  base  of  the 
windward  column  is 


where  w  equals  the  wind  load  per  foot  of  height. 

To  find  V  we  will  take  moments  about  the  leeward  column.  The 
moments  Mb  and  Mbi  at  the  bases  of  the  columns  respectively,  resist 
overturning  and  we  have 


and  since  H=  — 


(44) 


Now  if   -  is  taken  equal  to  y0,  we  have  after  transposing 


'=—yi  =  L[2/f—wy0l  I  '— •*»    |  (45) 

'  u  J  r»  \        / 


It  will  be  seen  that  (45)  is  the  same  value  of  V  and  F1  that  we 
would  obtain  if  the  bent  were  hinged  at  the  point  of  contra-flexure. 

From  (43)  and  (45)  it  will  be  seen  that  we  can  consider  the  col- 
umns as  hinged  at  the  point  of  contra-flexure  and  solve  the  problem 
as  in  Case  I,  taking  into  account  the  wind  above  the  point  of  contra- 
flexure  only.  The  maximum  shear  in  the  column  is  shown  in  (d) 
Fig.  52. 

The  maximum  positive  moment  occurs  at  the  foot  of  the  leeward 
knee  brace  and  is  Mk  =  H  (d  —  y0)  ;  the  maximum  negative  moment 
occurs  at  the  base  of  the  leeward  column  and  is  equal  to  Mb  =  H  y0. 


COLUMNS  FIXED  AT  THE  BASE  91 

The  maximum  fibre  stress  occurs  at  the  foot  of  the  knee  brace, 
and  is  given  by  the  formula 


f  A-f  - 

'  ~ 


P  My 


(30a) 


E 

The  nomenclature  being  the  same  as  for  (30)  except  h,  which 
is  the  distance  in  inches  from  the  point  of  contra-flexure  to  the  top  of 
the  column. 


(2)     Columns  fixed  at  the  base  and  top. — In  this  case  it  can  be 
by  inspection  that  tl 
and  we  have  for  this  case 


seen  by  inspection  that  the  point  of  inflection  is  at  a  point  y0  = 


B  =  &  +  C  (3ia) 

*  =  ——  =  Af*  (32a) 


It  is  difficult  to  realize  the  exact  conditions  in  either  (l)  or  (2), 
in  Case  II,  and  it  is  probable  that  when  an  attempt  is  made  to  fix 
columns  at  the  base,  the  actual  conditions  lie  some  place  between  (i) 
and  (2).  It  would  therefore  seem  reasonable  to  assume  the  minimum 
value,  3'0  =  —  -  as  the  best  value  to  use  in  practice.  This  assumption  is 
commonly  made  and  will  be  made  in  the  problems  which  follow. 

Having  the  external  forces  H1,  B,  C  and  F1  the  stresses  K,  U  and 
L  are  computed  by  formulas  (27),  (28)  and  (29).  The  remaining 
stresses  'in  the  truss  can  then  be  computed  by  the  ordinary  algebraic  or 
graphic  methods. 

For  a  simple  graphic  solution  of  this  problem,  where  the  ex- 
ternal forces  B  and  C  are  not  computed,  see  Fig.  55  and  Fig.  57. 

Maximum  Stresses.  —  It  is  not  probable  that  the  maximum 
snow  and  wind  loads  will  ever  come  on  the  building  at  the  same  time, 
and  it  is  therefore  not  necessary  to  design  the  structure  for  the  sum  of  the 
maximum  stresses  due  to  dead  load,  snow  load  and  wind  load.  A 


92  STRESSES  IN  A  TRANSVERSE  BENT 

common  method  is  to  combine  the  dead  load  stresses  with  the  snow 
or  the  wind  load  stresses  that  will  produce  maximum  stresses  in  the 
members.  It  is,  however,  the  practice  of  the  author  to  consider  that 
a  heavy  sleet  may  be  on  the  roof  at  the  time  of  a  heavy  wind,  and  to 
design  the  structure  for  the  maximum  stresses  caused  by  dead  and  snow 
load ;  dead  load,  minimum  snow  load  and  wind  load ;  or  dead  load  and 
wind  load.  It  should  be  noted  that  the  maximum  reversals  occur  when 
the  dead  and  wind  load  are  acting.  For  a  comparison  of  the  stresses 
due  to  the  different  combinations  see  Table  VI. 

A  common  method  of  computing  the  stresses  in  a  truss  of  the 
Fink  type  for  small  steel  frame  mill  buildings  is  to  use  an  equivalent  uni- 
form vertical  dead  load ;  the  knee  braces  and  the  members  affected 
directly  by  the  knee  braces  being  designed  according  to  the  judgment 
of  the  engineer.  This  method  is  satisfactory  and  expeditious  when 
used  by  an  experienced  man,  but  like  other  short  cuts  is  dangerous 
when  used  by  the  inexperienced.  For  a  comparison  of  the  stresses  in 
a  6o-foot  Fink  truss  by  the  exact  and  the  approximate  method  above, 
see  Table  VI. 

Stresses  in  End  Framing. — The  external  wind  force  on  an  end 
bent  will  be  one-half  what  it  would  be  on  an  intermediate  trans- 
verse bent,  and  the  shear  in  the  columns  may  be  taken  as  equal  to  the  to- 
tal external  wind  force  divided  by  the  number  of  columns  in  the  braced 
panels.  The  stresses  in  the  diagonal  rods  in  the  end  framing,  as  in  Fig. 
I,  will  then  be  equal  to  the  external  wind  force  H,  divided  by  the  number 
of  braced  panels,  multiplied  by  the  secant  of  the  angle  the  diagonal  rod 
makes  with  a  vertical  line  (For  analysis  of  Portal  Bracing  see  Chapter 
XII). 

Bracing  in  the  Upper  Chord  and  Sides.— The  intensity  of 
the  wind  pressure  is  taken  the  same  on  the  ends  as  on  the  sides, 
and  the  wind  loads  are  applied  at  the  bracing  connection  points  along  the 
end  rafters  and  the  corner  columns.  The  shear  transferred  by  each 
braced  panel  is  equal  to  the  total  shear  divided  by  the  number  of  braced 
panels.  The  stresses  in  the  diagonals  in  each  braced  panel  are  com- 


GRAPHIC  CALCULATION  OF  STRESSES  93 

puted  by  applying  wind  loads  at  the  points  above  referred  to,  the  wind 
loads  being  equal  to  the  total  wind  loads  divided  by  the  number  of 
panels.  The  stresses  are  computed  as  in  a  cantilever  truss.  The  brac- 
ing in  the  plane  of  the  lower  chord  is  designed  to  prevent  undue  de- 
flection of  the  end  columns  and  to  brace  the  lower  chords  of  the  trusses. 
All  \vind  braces  should  be  designed  for,  say,  5,000  pounds  initial  stress 
in  each  member,  and  the  struts  and  connections  should  be  proportioned 
to  take  the  resulting  stresses. 

It  should  be  noted  that  a  mill  building  can  be  braced  so  as  to  be 
rigid  without  knee  braces  if  the  bracing  be  made  sufficiently  strong. 

GRAPHIC  CALCULATION  OF  STRESSES.— Data.— To  il- 
lustrate the  method  of  calculating  the  stresses  in  a  transverse  bent  by 
graphic  methods,  the  following  data  for  a  transformer  building  similar 
to  one  designed  by  the  author  will  be  taken. 

The  building  will  consist  of  a  rigid  steel  frame  covered  with  cor- 
rugated steel  and  will  have  the  following  dimensions:  Length  of 
building,  80'  o";  width  of  building,  60'  o";  height  of  columns, 
20'  o";  pitch  of  truss,  l/4  (6"  in  12");  total  height  of  building, 
35'  o";  the  trusses  will  be  spaced  16'  o"  center  to  center.  The  trusses 
will  be  riveted  Fink  trusses.  Purlins  will  be  placed  at  the  panel  points 
of  the  trusses  and  will  be  spaced  for  a  normal  roof  load  of  30  Ibs.  per 
square  foot.  The  roof  covering  will  consist  of  No.  20  corrugated  steel 
with  2 1/2  -inch  corrugations,  laid  with  6-inch  end  laps  and  two  cor- 
rugations side  lap,  with  anti-condensation  lining  (see  Chapter  XVIII). 
The  side  covering  will  consist  of  an  outside  covering  of  No.  22  corru- 
gated steel  with  2l/2 -inch  corrugations,  laid  with  4-inch  end  laps  and 
one  corrugation  side  lap;  and  an  inside  lining  of  No.  24  corrugated 
steel  with  i^/J-inch  corrugations,  laid  with  4-inch  end  laps  and  one 
corrugation  side  lap.  For  additional  warmth  two  layers  of  tar  paper 
will  be  put  inside  of  the  lining.  Three  36-inch  Star  ventilators  placed 
on  the  ridge  of  the  roof  will  be  used  for  ventilation.  The  general  ar- 
rangement of  the  framing  and  bracing  will  be  as  in  Fig.  I  and  Fig.  81. 


94  STRESSES  IN  A  TRANSVERSE  BENT 

The  approximate  weight  of  the  roof  per  square  foot  of  horizontal 
projection  will  be  as  follows : 

Trusses    3.6  Ibs.  per  sq.  ft. 

Purlins  and  Bracing 3.0     "      "  "  " 

Corrugated  Steel    2.4     "       "  "  " 

Roof  Lining  i.o    "      "  "  " 


Total 10. o 

The  maximum  snow  load  will  be  taken  at  20  pounds,  and  the 
minimum  snow  load  at  10  pounds  per  square  foot  of  horizontal  pro- 
jection of  roof. 

The  wind  load  will  be  taken  at  20  pounds  per  square  foot  on  a 
vertical  projection  for  the  sides  and  ends  of  the  building,  20  pounds 
per  square  foot  on  a  vertical  surface  when  the  wind  is  considered  as 
acting  horizontally  on  the  vertical  projection  of  the  roof,  and  30 
pounds  per  square  foot  on  a  vertical  surface  when  the  wind  is  consid- 
ered as  acting  normal  to  the  roof. 

The  stresses  in  an  intermediate  transverse  bent  will  be  calculated 
for  the  following: 

CASE  i.     Permanent  dead  and  snow  loads. 

CASE  2.  A  horizontal  wind  load  of  20  pounds  per  square  foot  on 
the  sides  and  vertical  projections  of  the  roof,  with  the  columns  hinged 
at  the  base. 

CASE  3.  Same  wind  load  as  in  Case  2,  with  columns  fixed  at  the 
base. 

CASE  4.  A  horizontal  wind  load  of  20  pounds  per  square  foot  on 
the  sides,  and  the  normal  component  of  a  horizontal  wind  load  of  30 
pounds  per  square  foot  on  the  roof,  with  columns  hinged  at  the  base. 

CASE  5.  Same  wind  load  as  in  Case  4,  with  columns  fixed  at 
the  base. 

Case  i.  Permanent  Dead  and  Snow  Load  Stresses. — On  ac- 
count of  the  limited  size  of  the  stress  diagram  the  secondary  members 
have  been  omitted  and  the  loads  applied  as  shown  in  Fig.  53.  The 


DEAD  AND  SNOW  LOAD  STRESSES 


95 


loads  producing  stresses  in  the  truss  are  laid  off  to  the  prescribed  scale, 
,\\-y  being  the  left,  and  y-*8  the  right  reaction.  The  stresses  are  cal- 
culated as  follows:  Beginning  with  the  left  reaction,  x^-y,  draw  lines 
through  x^  and  y,  parallel  to  the  upper  and  lower  chords  of  the  truss, 
respectively,  and  the  line  x^-2.  will  represent  the  compressive  stress  in 
the  member  .\\-2.  and  y-2  will  represent  the  tensile  stress  in  the  member 
y-2  to  the  scale  of  the  stress  diagram. 


15      20" 


-*-- 


c-toc- 

Lenqthof  Buidinq.800"c-toc- 
Distance  C-TOC  -Trusses  ,16-0* 
Height  of  Columns  20'-Q" 
Pitch  of  Roof  i(6"m  12") 

60-0" 


CASE   I 

Dead  Load  lOlbs  persq-fr  nor-  projection 
Dead  Load  Stress  Diaqram 

0  ^000        4000         6000 


Compression 
Tension 


Snow  Load  <?OlbS  persqft  horproj 
Snow  Load  Stress  Diaqram 

0  4000         80OO        12000 


FIG.  53.    DEAD  AND  SNOW  LOAD  STRESS  DIAGRAM. 

Calculate  the  stresses  in  the  remaining  members  in  like  manner, 
being  careful  to  take  the  members  in  order  around  a  joint  in  com- 
pleting any  polygon.  The  indeterminate  case  at  the  joint  U2,  can  be 


96  STRESSES  IN  A  TRANSVERSE  BENT 

solved  by  calculating  the  stress  in  5-6  and  substituting  it  in  the  diagram, 
or  by  substituting  an  auxiliary  member  as  shown.  Compression  and 
tension  in  the  truss  and  stress  diagram  in  Fig.  53  are  indicated  by  heavy 
and  light  lines  respecti\ely. 

The  stress  in  each  column  is  equal  to  one-half  the  sum  of  the  ver- 
tical loads,  plus  the  load  carried  directly  by  the  column. 

Case  2.  Wind  Load  Stresses:  Wind  Horizontal;  Columns 
Hinged. — The  wind  will  be  considered  as  acting  at  the  joints,  as  shown 
in  Fig.  54.  Replace  the  columns  with  trusses  as  indicated  by  the  dotted 
lines.  This  makes  the  bent  a  two-hinged  arch  (see  Chapter  XIV),  and 
the  stresses  will  be  statically  determinate  as  soon  as  the  horizontal  reac- 
tions H  and  H1  at  the  bases  of  the  columns,  have  been  determined.  The 
usual  assumption  in  mill  buildings  and  portals  of  bridges  is  that 
H  =  H1  =  ™  where  W  —  the  horizontal  component  of  the  external 
wind  force  (see  Chapter  XII).  To  calculate  V  and  F1  graphically,  pro- 
duce the  line  of  resultant  wind  until  it  inersects  a  vertical  line  through 
the  center  of  the  truss,  and  connect  the  intersection  A  with  the  bases  of 
the  columns  B  and  C.  From  A  lay  off  H  =  H1  =  -=-,  as  shown  in 
Fig.  54,  and  complete  the  triangles  by  drawing  vertical  lines  through 
the  ends  of  these  lines.  The  vertical  closing  lines  will  be  V  =  —  F1, 
as  shown  in  Fig.  54. 

The  stresses  are  calculated  as  follows:  Beginning  with  the  foot 
of  the  column  B,  lay  off  the  dotted  line  A-B  =  R.  At  B,  lay  off  the 
load  a-B  =  224.0  Ibs. ;  through  a  draw  a  line  parallel  to  auxiliary  truss 
member  a-b,  and  through  A  draw  a  line  parallel  to  the  column  b-A, 
completing  the  polygon  A-B-a-b. 

The  line  a-b  in  the  stress  diagram  will  be  the  compression  in  the 
auxiliary  member  a-b,  and  A-b  will  be  the  tension  in  the  column  A-b. 
It  should  be  noted  that  V  is  equal  to  the  algebraic  sum  of  the  vertical 
components  of  the  stresses  in  a-b  and  A-b.  Next  lay  off  x-a  =  3200  Ibs. 
and  complete  the  polygon  a-x-c-b  by  drawing  lines  through  x  and  b  par- 
allel to  the  auxiliary  truss  members  x-c  and  b-c  respectively.  In  like 
manner  determine  the  stresses  at  the  foot  of  the  knee  brace  bv  con- 


WIND  LOAD  STRESSES,  CASE  2 


97 


structing  the  polygon  A-b-c-i ;  and  at  the  top  of  the  column  by  con- 
structing the  polygon  c-x-x-2-i,  etc.,  until  the  diagram  is  checked  up  at  C 
with  C-A  =  R1.  The  indeterminate  case  at  the  joint  £72,  can  De  solved 


15     ^o 


Wind  liaOOIbS 


a 


CASE  2 

Columns  Pin  Connected 
Maximum  Mom- in  Col  =940800  in-lbs 


17     / 


6 


Wind  Load  Stress  Diagram 

Wind  Horizontal,  20  IDS  persqfT 

O  4OOO  8000 


6  4  A 

FIG.  54.    WIND  LOAD  STRESS  DIAGRAM,  CASE  2. 

by  computing  the  stress  in  5-6  (component  due  to  stress  in  6-7),  and 
substituting  it  in  the  diagram,  or  by  substituting  an  auxiliary  member. 

The  stresses  in  the  auxiliary  members  are  represented  by  dotted 
lines  and  are  of  no  value  in  designing  the  bent.  It  should  be  noted 
that  the  auxiliary  members  do  not  affect  the  stresses  in  the  trusses  and 
knee  braces,  which  are  correctly  given  in  the  stress  diagram. 

The  maximum  stress  in  the  knee  brace  A-i$  is  compression,  and 
occurs  on  the  leeward  side. 


98 


STRESSES  IN  A  TRANSVERSE  BENT 


The  maximum  shear  in  the  leeward  column  below  the  knee  brace  is 
H1  =  5600  Ibs. ;  the  maximum  shear  above  the  knee  brace  is  13,100  Ibs. 
The  maximum  moment  occurs  at  the  foot  of  the  knee  brace  and  is 
H1  x  14  x  12  =  940,800  inch-lbs. 

Case  3.  Wind  Load  Stresses:  Wind  Horizontal;  Columns 
Fixed  at  Base. — This  is  Case  2  with  the  base  of  the  column  hinged  at 
the  point  of  contra-flexure.  In  calculating  H  and  V,  Fig.  55,  the  wind 


600 


Columns  Fixed  at  Base 
Max-Mom-  in  Col-  =  376320  in-  Ibs 


2240 


Wind  Load  Stress  Diagram 
Wind  Horizontal  20  IbS-per  sq-ff 
15        0  4000  6000 


Compression 
Tension 


16 


^mzJT5' 


\2  &  4  A 

FIG.  55.   WIND  LOAD  STRESS  DIAGRAM,  CASE  3. 

above  the  point  of  contra-flexure  only  (see  formula  (45))  produces 
stresses  in  the  bent.  The  value  of  fixing  the  columns  at  the  base  is 
seen  by  comparing  the  stresses  in  Case  2  with  those  in  Case  3,  both 
being  drawn  to  the  same  scale.  Maximum  shear  in  the  leeward  column 
below  the  knee  brace  is  H1  =  4480  Ibs. ;  above  the  knee  brace  is  5230 
Ibs.  The  maximum  positive  moment  occurs  at  the  foot  of  the  knee 
brace  and  negative  moment  at  the  foot  of  the  column,  and  is  H1  x  7 
x  12  =  376,320  inch-lbs. 


WIND  LOAD  STRESSES,  CASE  4 


99 


Case  4.    Wind  Load  Stresses :  Wind  Normal ;  Columns  Hinged. 

— In  Fig.  56  the  resultant  of  the  external  wind  forces  on  the  sides  and 
the  roof  acts  through  their  intersection,  and  is  parallel  to  C  B  in  the 
stress  diagram  (line  C  B  is  not  drawn).  To  calculate  V  and  F1  con- 
nect the  point  of  intersection,  A,  of  the  resultant  wind  and  the  vertical 
line  through  the  center  of  truss,  with  the  bases  of  the  columns  B  and  C. 


960 


Wind  6400 


£L 
\      b 


\  Columns  Pm  Connected 

iMox-  Mom  in  Col-324000  in  Ibs 


CASE  4 

Wind  Load  Stress  Diaqram 

Wind  Normal.Roof  18  Ibs- Sides 20 Ibs  sq'f* 


sec: 


16 


FIG.  56.    WIND  LOAD  STRESS  DIAGRAM,  CASE  4. 


100 


STRESSES  IN  A  TRANSVERSE  BENT 


From  A  lay  off  one-half  of  resultant  wind  on  each  side,  and  from  the 
extreme  ends  drop  vertical  lines  V  and  V1  to  the  dotted  lines  A  B  and 
A  C.  The  vertical  lines  V  and  F1  will  be  the  vertical  reactions,  the 
horizontal  lines  will  be  H  and  H1,  and  R  and  Rl  will  be  the  resultants 
of  the  horizontal  and  vertical  reactions  at  B  and  C  respectively.  The 
stresses  are  calculated  by  beginning  at  the  base  of  the  column  B  as  in 
Case  2.  In  the  polygon  a-B-A-b  at  B,  A-B  =  R,  a-B  =  2240  Ibs.,  and 
a-&  and  A-b  are  the  stresses  in  a-b  and  A-b  respectively. 


3080 


CASE  5 

Wind  Load  Stress  Diagram 

Wind  Normal,  Roof  18  Ibs  Sides  20  Ibs-  sq-fr, 


4000 


Compression 
Tension 


x      o  a 
FIG.  57.   WIND  LOAD  STRESS  DIAGRAM,  CASE  5. 


WIND  LOAD  STRESSES,  CASJB  5 


The  maximum  shear  in  the  leeward  column  below  the  knee  brace 
is  H1  =  5500  Ibs.,  above  the  knee  "brace  is  12,806  Ibs. ;  the  maximum 
moment  occurs  at  the  foot  of  the  knee  brace  and  isH1xi4Xi2  = 
924,000  inch-lbs. 

Case  5.  Wind  Load  Stresses:  Wind  Normal;  Columns  Fixed 
at  Base. — This  is  Case  4  with  the  base  of  the  column  moved  up  to  the 
point  of  contra-flexure.  The  maximum  shear  in  the  leeward  column 
below  the  knee  brace  is  4300  Ibs.,  above  the  knee  brace  is  5000  Ibs. ;  the 
maximum  positive  moment  occurs  at  the  foot  of  the  knee  brace  and 
negative  moment  at  the  foot  of  the  column  and  is  H1  x  7  x  12  =  361,200 
inch-lbs.  For  analysis  see  Fig.  57. 

Maximum  Stresses. — The  stresses  in  the  different  members 
of  the  bent  for  the  different  cases  are  given  in  Table  V.  The  maximum 

TABLE  V. 


m 


A,\ 


Name 
of 
Piece 

Stresses  in  a  Bent  For 

Dead 
Load 

Snow 
Load 

Wind     Load 

Case2 

Case3 

Case  4 

Case  5 

X-2 

-1-9300 

+I89OO 

+3700 

+290O 

+/54OO 

+14900 

X-3 

+8800 

+I76OO 

+4900 

+40OO 

+I54OO 

+14900 

X-6 

+  8200 

+/6400 

+  4OO 

+  14  OO 

+10200 

+IIZOO 

X-7 

+  7700 

+15400 

+1400 

+3400 

+10200 

+II20O 

X-9 

+7700 

+I54OO 

-6100 

-I90O 

-  1400 

+  2800 

X-13 

+9500 

i-/8600 

-I9d00 

-3600 

-14600 

-3600 

1-2 

-6300 

-/6600 

+  5700 

+2800 

-  5100 

-8000 

2-3 

+1100 

+  2200 

+   50O 

+  500 

+  2400 

+2400 

3-4- 

-1200 

-24OO 

-6800 

-4900 

-8500 

-6700 

4-5 

+22OO 

+  4400 

+3QOO 

+3000 

+  7300 

+  6600 

5-6 

-I20O 

-2400 

-  600 

-    600 

-2600 

-2600 

6-7 

+1100 

+  2200 

+  500 

+  50O 

+24OO 

+2400 

5-8 

-24OO 

-480O 

-4500 

-33  OO 

-8200 

-7400 

7-8 

-5600 

-  7200 

-4900 

-3900 

-IO800 

-IOOOO 

8-9 

-3600 

-  7200 

+7500 

+3600 

+  7400 

+35OO 

9-12 

+2200 

i>44OO 

-6700 

-3200 

-6700 

-3200 

12-13 

-/200 

-2400 

+/5200 

+  7400 

+14800 

+  7000 

Y-4- 

-7IOO 

-14200 

+2400 

+  800 

-6000 

-7700 

Y-8 

-47OO 

-  7400 

+6600 

+40OO 

+  2200 

-  4OO 

Y-12 

-7/00 

-14200 

+/4200 

+  7700 

+  970O 

+2100 

13-15 

-8300 

-/6600 

+4600 

+3000 

+  5OO 

-/300 

A-l 

-9000 

-6200 

-8500 

-6700 

A-15 

+22300 

+/IOOO 

+21500 

+/0400 

A-b 

+480O 

+  9600 

-3200 

-2100 

+  340O 

+4500 

C-l 

+460O 

+  9600 

+  1700 

+/30O 

+  8OOO 

+  7600 

A-17 

+4600 

+  9600 

i-3200 

+2100 

+5500 

+  4/OO 

15-16 

+4800 

+  9600 

-8600 

-3800 

-6400 

-2400 

S'  i  $Tfei&3SEs:iN  A  TRANSVERSE  BENT 


stresses  in  the  different  members  of  the  bent  for  ( i )  dead  load  plus  max- 
imum snow  load;  (2)  dead  load  plus  wind  load,  Case  4;  (3)  dead  load 
plus  minimum  snow  load  plus  wind  load,  Case  4;  and  (4)  a  vertical 
dead  load  of  40  Ibs.  per  sq.  ft.  horizontal  projection  of  the  roof  are  given 
in  Table  VI.  The  stresses  which  control  the  design  of  the  members 
may  be  seen  in  Table  VI.  By  comparing  these  values  with  the  stresses 
given  in  the  last  column  the  accuracy  of  the  equivalent  load  method  can 
be  seen. 

TABLE  VI. 


Maximum  Stresses  ina  Bent  For 

Name 
of 
Piece 

Dead  Load  + 
fMaxSnow 
Load 

Dead  Load  + 
Wind  Load 
Case  A- 

DeadLoad+Min- 
SnowLoacH-Wind 
Load-  Case  4- 

Vert-Dead  Load 
of  40  Ibs-  per  Sq- 
FT-ofHor-Proj- 

x-2 

+28200 

+24700 

+343OO 

+  372  OO 

X-3 

+26400 

+24EOO 

+33OOO 

+  35200 

X-6 

+264OO 

+I84OO 

+266OO 

+32800 

X-7 

+23100 

+17900 

+256OO 

+3OdOO 

X-9 

+23IOO 

+  6300 

+  /4000 

+3O8OO 

X-J3 

+28200 

-  530O 

+  4000 

+  37200 

1-2 

-24900 

-I34OO 

-2I7OO 

-33200 

2-3 

+  3300 

+  3SOO 

+  4600 

+  44  OO 

3-4 

-3600 

-9700 

-/O90O 

-  4-800 

4-5 

+  6600 

+  9500 

+  117  OO 

+  8800 

5-6 

-  3600 

-5800 

-  5OOO 

-4-800 

6-7 

+  3300 

+  35OO 

+  460O 

+  4-4OO 

5-8 

-7200 

-/O600 

-/300O 

-9600 

7-8 

-10800 

-14400 

-/8000 

-/44-OO 

8-9 

-/O800 

+  3600 

+     200 

-/44OO 

9-12 

+  6  600 

-4500 

-2300 

+  880O 

12-13 

-3600 

+/360O 

+/2400 

-4800 

Y-4 

-2/300 

-/3/OO 

-20200 

-2840O 

Y-8 

-141  OO 

-2500 

-    5200 

-I4-8OO 

Y-12 

-23  /oo 

+  26OO 

-  45OO 

-28400 

I3-J5 

-24900 

-  78OO 

-/6IOO 

-32400 

A-l 

-8500 

-  850O 

A-15 

+2/500 

-2/50O 

A-b 

+/4400 

+  8200 

+/30OO 

+/92OO 

C-l 

+14400 

+/28OO 

+/7600 

+  /9200 

A-  17 

+14400 

+(0100 

+/4900 

+/92OO 

15-16 

+/44OO 

-  /600 

+  3200 

+  /9200 

CALCULATION  OF  REACTIONS 


103 


Graphic  Calculation  of  Reactions. — The  graphic  method  for 
calculating  the  reactions  given  in  Fig.  56  and  Fig.  57  may  be  proved 
as  follows:  In  Fig.  5/a  the  intersection  of  3  W  and  the  center  line 
of  the  bent  is  at  A.  Draw  A-B  and  A-C,  lay  off  2  W  so  that  it  is 
bisected  by  the  point  A,  and  draw  1-2  and  3-4.  Then  1-2  equals  V 
and  3-4  equals  V  as  shown  in  the  following  proof : 

Proof. — To  calculate  V  take  moments  of  external  forces  about 
C,  and 


V  =•• 


4  times  area  triangle  A-^- 


But  area  triangle  A-^-C  is  also  equal  to 

3-4  XL 


3-4 


and 


=  3-4 


which  proves 

1-2  =  V. 


the  construction.    It  may  be  proved  in  like  manner  that 


TRANSVERSE  BENT  WITH  VENTILATOR.— The  calcu- 
lation of  the  wind  stresses  in  a  transverse  bent  with  a  monitor  venti- 
lator is  shown  in  Fig.  5?b.  The  bents  are  spaced  32'  o"  centers  and 


io4 


STRESSES  IN  A  TRANSVERSE  BENT 


are  designed  for  a  horizontal  wind  load  of  20  Ibs.  per  sq.  ft.,  the  nor- 
mal wind  roof  load  being  obtained  by  Hutton's  formula  as  shown  in 
Fig.  6. 

The  point  of  contra-flexure  is  found  by  substituting  in  formula 
(41)  to  be  at  a  point  ;y0  =  17.0'.  The  external  forces  are  calculated  for 
the  bent  above  the  point  of  contra-flexure  by  multiplying  the  area  sup- 
ported at  the  point  by  the  intensity  of  the  wind  pressure.  For  example, 
the  load  at  B  is  32'  X  6.75'  X  20  Ibs.  =  4320  Ibs. 


Trusses 32-0  c.foc. 
Dead  Load'  20  Ib.  sq.ft.  hor. 
Wind  Load- 20 Ib.    "  "  vert: 

0     5000  10000        20000 

Scale  Stresses 

•\j 

&  8  A 

WIND  LOAD  5TRE55  D/AGRAM 
COLUMNS  r~/x£O 

FIG.  57b. 

The  line  of  application  and  the  amount  of  the  external  wind  load, 
2  W,  is  found  by  means  of  a  force  and  an  equilibrium  polygon.  2  W 
acts  through  the  intersection  of  the  strings  parallel  to  the  rays  O-B 


BENT  WITH  SIDE  SHEDS  105 

and  O-C,  and  is  equal  to  C-B  (line  C-B  is  not  drawn  in  force  polygon) 
in  amount.  The  reactions  R  and  Rf  are  calculated  by  the  graphic 
method  as  previously  described. 

The  calculation  of  stresses  is  begun  at  point  B  in  the  windward 
column,  and  in  the  stress  diagram  the  stresses  at  B  are  found  by 
drawing  the  force  polygon  ar-B-A-b-a.  The  remaining  stresses  are 
calculated  as  for  a  simple  truss.  In  calculating  the  stresses  in  the 
ventilator  it  was  assumed  that  diagonals  9-10  and  10-12  are  tension 
members,  so  that  9-10  will  not  be  in  action  when  the  wind  is  acting  as 
shown.  Before  solving  the  stresses  at  the  joint  6-7-9  ^  was  necessary 
to  calculate  the  stresses  in  members  t-n,  10-11,  and  o-/t.  The  re- 
mainder of  the  solution  offers  no  difficulty  to  one  familiar  with  the 
principles  of  graphic  statics. 

The  stress  in  post  b-a  is  equal  to  V ,  while  the  stress  in  i-c  is  found 
by  extending  i—c  to  c'  in  the  stress  diagram,  c'  being  a  point  on  the  load 
line.  The  stress  in  post  t^-A  is  equal  to  V ,  while  the  stress  in  10,-w  is 
found  by  extending  1 9-7/1  to  m'  in  the  stress  diagram,  m'  being  a  point  on 
the  horizontal  line  drawn  through  C.  The  kind  of  stress  in  the  different 
members  is  shown  by  the  weight  of  lines  in  the  bent  diagram  and  by 
arrows  in  the  stress  diagram,  one  arrow  indicating  the  direction  and  kind 
of  stress  the  first  time  a  stress  is  used  and  two  arrows  indicating  the 
second  time  a  stress  is  used. 

TRANSVERSE  BENT  WITH  SIDE  SHEDS.— Transverse 
bents  with  side  sheds  are  quite  often  used  in  the  design  of  shops  and 
mills.  The  calculation  of  the  stresses  due  to  wind  load  in  a  bent  of  this 
type  is  an  interesting  application  of  the  author's  graphic  solution  of 
stresses  in  transverse  bents. 

It  is  required  to  calculate  the  stresses  due  to  a  horizontal  wind 
load  of  30  Ibs.  per  square  foot  on  the  sides  and  the  normal  component 
of  30  Ibs.  (Hutton's  Formula,  Fig.  6)  on  the  roof,  the  bents  being 
spaced  20'  o"  centers,  as  in  Fig.  57c.  The  loads  are  calculated,  and  by 
means  of  a  force  polygon  in  (d)  and  an  equilibrium  polygon  in  (a) 
the  resultant  wind  5  W  is  found  to  pass  through  point  E,  and  to  be 
equal  to  30,800  Ibs. 

Calculation  of  Reactions. — The  horizontal  shear  of  25,400  Ibs. 
will  be  taken  by  the  columns  in  proportion  to  their  rigidities,  in  this 


ic6  STRESSES  IN  A  TRANSVERSE  BENT 

case  the  rigidities  of  the  columns  are  assumed  equal  and  the  shear  at 
the  foot  of  each  column  will  be  6350  Ibs.  The  vertical  reactions  will 
be  due  to  two  forces:  (i)  a  vertical  load  of  17,200  Ibs.,  which  will  be 
taken  equally  by  the  four  columns,  making  a  load  of  4300  Ibs.  on  each ; 
and  (2)  to  a  bending  moment  of  25,400  Ibs.  X  9-2  ft.  =  233,680  ft.-lbs. 
(the  bending  moment  about  C.  G.  is  also  equal  to  30,800  Ibs  X  7-6  ft.), 
which  will  be  resisted  by  the  columns  and  will  cause  reactions  varying 
as  the  distance  from  the  center  of  gravity  of  the  columns,  (E),  as  in  the 
case  of  the  continuous  portal,  Fig.  63. 

Let  v\,  v'2,  v'z,  and  v\  represent  the  reactions  due  to  moment  in 
the  columns,  respectively;  then  if  a  is  the  reaction  on  a  column  at  a 
units  distance  from  the  center  of  gravity  we  will  have  v\  =  —  a  40, 
v'2  =  —  a  20,  z/3  =  +  a  20,  and  v'±  =  -\-  a  40.  The  resisting  moment 
of  each  column  will  be  equal  to  the  reaction  multiplied  by  the  distance 
from  the  center  of  gravity,  and  a  40*  +  a  20*  +  a  2O2  +  a  40*  =  233,- 
680  ft.-lbs.  from  which  a  =  58.42  Ibs.  and  v\  =  —  2340  Ibs. ;  v\  =  — 
1170  Ibs. ;  z/3  =  -f  1170  Ibs. ;  z/4  =  -f-  2340  Ibs. 

Now  adding  the  reactions  due  to  (i)  and  (2)  we  have 

V^  =  4300  —  2340  =  +  1960  Ibs., 
F2  =  4300  —  1 170  =  +  3130  Ibs., 
Vz  =  4300  +  1 170  =  +  5470  Ibs., 
Vi  =  4300  +  2340  =  +  6640  Ibs. 

Combining  the  horizontal  and  vertical  reactions  we  have  R^  =  a^-A  = 
6600  Ibs.;  R2  =  A-B  =  7200  Ibs.;  #8  =  £-C  =  8400  Ibs.;  R±  = 
C-D  =  9100  Ibs.  These  reactions  close  the  force  polygon  in  (d). 

Calculation  of  Stresses. — Auxiliary  members  are  substituted  as 
shown  by  the  broken  lines.  It  will  be  seen  that  these  members  are 
arranged  so  that  all  bending  is  removed  from  the  columns  and  that 
the  stresses  in  the  truss  members  are  correctly  given  in  the  stress  dia- 
gram. The  calculation  is  started  at  point  A  at  the  foot  of  the  left- 
hand  column  as  in  the  case  of  the  simple  transverse  bent,  and  reac- 
tions R2  and  Rs  are  substituted  as  the  calculation  progresses,  the  stress 
diagram  finally  closing  at  the  base  of  the  leeward  column,  point  D. 
The  stresses  are  given  on  the  members  in  (a).  The  direct  stresses  in 
the  columns  are  easily  found  by  algebraic  resolution  beginning  at  the 


TRANSVERSE  BENT  WITH  SIDE  SHEDS. 


107 


loS  STRESSES  IN  A  TRANSVERSE  BENT 

foot  of  the  columns  where  the  direct  stress  is  equal  to  Vlt  F2,  F3  and 
F4,  respectively.  The  stresses  in  the  leeward  side  of  the  main  truss  are 
very  large  due  to  the  small  depth  of  truss  in  line  of  the  member  29-30. 
The  stresses  could  be  materially  reduced  and  a  considerable  saving  of 
material  obtained  by  using  a  main  truss  of  type  (b)  or  (h),  Fig.  88. 

Moment  and  Shear  in  Columns. — The  bending  moment  in  the 
main  leeward  column  is  shown  in  (b),  the  maximum  moment  is  at 
the  foot  of  the  knee  brace  and  is  M±  =  274,500  ft.-lbs.  The  shear  dia- 
gram is  shown  in  (c),  the  maximum  shear  is  between- the  foot  of  the 
knee  brace  and  the  top  of  the  column  and  is  S0  =  45,750  Ibs. 

NOTE. — The  stresses  in  a  bent  with  side  sheds  obtained  by  the  pre- 
ceding method  are  approximate  for  the  reason  that  the  assumed  condi- 
tions are  probably  never  entirely  realized.  In  the  exact  calculation  of 
the  stresses,  of  which  the  above  solution  is  the  first  approximation,  the 
deformation  of  the  framework  is  considered  in  a  manner  similar  to 
that  of  the  two-hinged  arch  in  Chapter  XIV.  The  approximate  solu- 
tion is  entirely  adequate  for  all  practical  purposes. 


CHAPTER  XII. 
STRESSES  IN  PORTALS. 

Introduction. — Portal  bracing  is  frequently  used  for  bracing  the 
sides  of  mill  buildings  and  open  sheds.  There  are  many  forms  of 
portal  bracing  in  use,  a  few  of  the  most  common  of  which  are  shown  in 
Fig.  58. 

H       5        F  R  I    H    6     F   R 


(a) 
I   H     6 


t 


Cd> 


6    f  e   ct  £  R 


X 

X 

X 

X 

f 
r 

c 

}< 

-J-. 

h  c 

9  — 

• 

r 

-x 

•A-i. 

cc) 


V1 


'+„     kaif/r   R 


(f) 


t 


/-*. 


Portal  bracing  may  be  in  separate  panels  or  may  be  continuous. 
The  columns  may  be  hinged  or  fixed  at  the  base  in  either 


case. 


no  STRESSES  IN  PORTALS 

CASE  I.  STRESSES  IN  SIMPLE  PORTALS:  Columns 
Hinged.  —  The  deflections  of  the  columns  in  the  portals  shown  in  Fig. 
58  are  assumed  to  be  equal  and 

H=H>=£ 

Taking  moments  about  the  foot  of  the  windward  column 

j/i  —  _  y  —  R  h 
s 

Having  found  the  external  forces,  the  stresses  in  the  members 
may  be  found  by  either  algebraic  or  graphic  methods. 

Algebraic  Solution.  —  Portal  (a).  —  To  obtain  the  stress  in  member 
G  C,  (a)  Fig.  58,  pass  a  section  cutting  G  F,  E  F  and  G  C,  and  take 
moments  of  the  external  forces  to  the  right  of  the  section  about  point  F 
as  a  center. 

(46) 


, 

(h  —  d}  sin  6 

But  H  =*  JLt    and  (h—  d)  sin  9  =  —  cos  9.    Substituting  these 

values  in  (46)  we  have 

GC=—     R'1     =  —  Fsece  (47) 

s  cose 

Resolving  at  C  and  F  we  have,  stress  in  £  F  —  o,  and  also  stresses 
£  £'  and  H  H'  =  o. 

To  obtain  stress  in  G  D,  pass  section  cutting  H  G,  HE'  and  G  D, 
and  take  moments  of  the  external  forces  to  the  left  of  the  section  about 
point  H  as  a  center. 


GD=  _       _  =-j-Fsece  (48) 

(h—  d)  sin  6  v 

To  obtain  stress  in  G  F,  pass  a  section  cutting  G  F,  H  F  and  G  Cs 
and  take  moments  of  the  external  forces  to  the  right  of  the  section 
about  point  C  as  a  center. 


_ 

h  -d  (49) 


ALGEBRAIC  SOLUTION  in 

To  obtain  stress  in  H  G,  pass  a  section  cutting  H  G,  H  E'  and  G  D, 
and  take  moments  of  the  external  forces  to  the  left  of  the  section  about 
the  point  D  as  a  center. 


HG  --  --.  (50) 

The  stress  in  the  windward  post,  A  F,  is  zero  above  and  V  below 
the  foot  of  the  knee  brace  C;  the  stress  in  the  leeward  post  is  zero  above 
and  V1  below  the  foot  of  the  knee  brace  D. 

The  shear  in  the  posts  is  H  below  the  foot  of  the  knee  brace,  and 
above  the  foot  of  the  knee  brace  is  given  by  the  formula 

S  =      Hd  '  -  =  stress  in  H  G  (51) 

h  —  d 

The  maximum  moment  in  the  posts  occurs  at  the  foot  of  the  knee 
braces  C  and  D  and  is 

M  =  Hd  (52) 

For  the  actual  stresses,  moments  and  shears  in  a  portal  of  this 
type,  see  Fig.  59. 

Portal  (b).  —  The  stresses  in  portal  (b)  Fig.  58,  are  found  in  the 
same  manner  as  in  portal  (a).  The  graphic  solution  of  a  similar  portal 
with  one  more  panel  is  given  in  Fig.  60,  which  see.  It  should  be 
noted  that  all  members  are  stressed  in  portals  (b)  and  (d). 

Portal  (c).  —  The  stresses  in  portal  (c)  Fig.  58,  may  be  obtained 
(i)  by  separating  the  portal  into  two  separate  portals  with  simple 
bracing,  the  stresses  found  by  calculating  the  separate  simple  portals 
with  a  load  =  y2  R  being  combined  algebraically,  to  give  the  stresses 
in  the  portal;  or  (2)  by  assuming  that  the  stresses  are  all  taken  by 
the  system  of  bracing  in  which  the  diagonal  ties  are  in  tension.  The 
latter  method  is  the  one  usually  employed  and  is  the  simpler. 

Maximum  moment,  shear,  and  stresses  in  the  columns  are  given 
by  the  same  formulas  as  in  (a)  Fig.  58. 

Portal  (e).—  In  portal  (e)  Fig.  58,  the  flanges  G  F  and  D  C  are 
assumed  to  take  all  the  bending  moment,  and  the  lattice  web  bracing 


1 1 2  STRESSES  IN  PORTALS 

is  assumed  to  take  all  the  shear.     The  maximum  compression  in  the 
upper  flange  G  F  occurs  at  F,  and  is 

(53) 

<54> 


h  —  d 
The  maximum  tension  in  the  upper  flange  G  F  is 

GF=  H  d 

The  maximum  stress  in  the  lower  flange  D  C  is 

D  C  =  Hh 

h  —  d 

maximum  tension  occurring  at  C,  and  maximum  compression  occurring 
at  D. 

The  maximum  shear  in  the  portal  strut  is  V ,  which  is  assumed  as 
taken  equally  by  the  lattice  members  cut  by  a  section,  as  a  a. 

Maximum  moment,  shear,  and  stresses  in  the  columns  are  given 
by  the  same  formulas  as  in  (a)  Fig.  58. 

Portal  (/). — The  maximum  moment  in  the  portal  strut  I  F  in  (f) 
Fig.  58,  occurs  at  H  and  G,  and  is 

M=  +  Hh  —  Va  (56) 

The  maximum  direct  stress  in  H  G  is  +  H,  and  in  I  H  is 

IH=-    hH_dd  (57) 

The  maximum  stress  in  G  F  is  given  by  formula  (49). 
The  maximum  shear  in  girder  I  F  is  equal  to  V.     The  stress  in  G  C 
is  —  H  h^(h-d)  sin 6  =  —  stress  H  D. 

Portal  strut  /  F  is  designed  as  a  girder  to  take  the  maximum 
moment,  shear  and  direct  stress. 

Maximum  moment,  shear,  and  stresses  in  the  columns  are  given 
by  the  same  formulas  as  in  (a)  Fig.  58. 

Graphic  Solution. — To  make  the  solution  of  the  stresses  statically 
determinate,  replace  the  columns  in  the  portal  with  trussed  framework 


GRAPHIC  SOLUTION 


as  in  Fig.  59.    The  stresses  in  the  interior  members  are  not  affected  by 
the  change  and  will  be  correctly  given  by  graphic  resolution. 


Hd  =  200o      G   -2000        F    +4000       E    R  =  2OOO 

h-d  "* ""     *~ 


/   6 


=         i    7 


bi 


I   ! 


IH-HOOO^B-^ 

|V=  300i 


'b 

I     /    -^ 

/        i 


'  I 

/  | 

f  I 

'A 4. 

V»3000 


Moment       Shear 


Portal 


2                                 1 

\  7 

\                / 
\              / 

\            ' 
\          / 
\        / 
\     / 

r  ^ 
\ 

\           / 

CASE  1 

Columns  Hinqed 

Stress   Diagram 
o         1000     eooo      5000 

"-       V  •' 

-7            \     / 

"V                a 

A        b              / 

,5 
Compression  —  — 
Tension            . 

As  before  H  = 


FIG.  59. 


and  F=-   F1  = 


Having  the  calculated  Jf,  J/1,  F^  and  F1,  the  stresses  are  calculated  by 
graphic  resolution  as  follows :  Beginning  at  the  base  of -the  column  A, 
lay  off  A-4  =  V  =  3000  Ibs.  acting  downward,  and  A-a  =  H  =  1000 
Ibs.  acting  to  the  right.  Then  a-i  and  4-1  are  the  stresses  in  members 
a- 1  and  4-1,  respectively,  heavy  lines  indicating  compression  and  light 
lines  tension.  At  joint  in  auxiliary  truss  to  right  of  C  the  stress  in  i-a 
is  known  and  stresses  in  1-2  and  2-0  are  found  by  closing  the  polygon. 


STRESSES  IN  PORTALS 


The  stresses  in  the  remaining  members  are  found  in  like  manner,  taking 
joints  C,  E,  F,  etc.  in  order,  and  finally  checking  up  at  the  base  of  the 
column  B.  The  full  lines  in  the  stress  diagram  represent  stresses  in 
the  portal ;  the  dotted  lines  represent  stresses  in  the  auxiliary  members 
or  stresses  in  members  due  to  auxiliary  members,  and  are  of  no  con- 
sequence. The  shears  and  moments  are  shown  in  the  diagram. 


Moment    Shear 


i- --4- 


CASE  I 

Columns  Hinged 

Stress  Diagram 
1000    zooo   3000 


Compression 
Tension 


FIG.  60. 

Simple  Portal  as  a  Three-Hinged  Arch. — In  a  simple  portal  the 
resultant  reactions  and  the  external  load  R  meet  in  a  point  at  the  mid- 
dle of  the  top  strut,  and  the  portal  then  becomes  a  three-hinged  arch 


COLUMNS  FIXED,  ALGEBRAIC  SOLUTION  115 

(see  Chapter  XIII),  provided  there  is  a  joint  at  that  point  (point  b, 
Fig.  60). 

In  Fig.  60  the  reactions  were  calculated  graphically  and  the  stresses 
in  the  portal  were  calculated  by  graphic  resolution.  Full  lines  in  the 
stress  diagram  represent  required  stresses  in  the  members.  Stresses 
3-2  and  11-12  were  determined  by  dropping  verticals  from  points  3  and 
ii  to  the  load  line  4-10. 

CASE  II.     STRESSES  IN  SIMPLE  PORTALS:   Columns 

Fixed.  —  The  calculation  of  the  stresses  in  a  portal  with  columns  fixed 
at  the  base  is  similar  to  the  calculation  of  stresses  in  a  transverse  bent 
with  columns  fixed  at  the  base.  The  point  of  contra-flexure  is  at  the 
point 

d 


measured  up  from  the  base  of  the  column.  The  point  of  contra-flexure 
is  usually  taken  at  a  point  a  distance  -—•  above  the  bases  of  the  columns. 

2 

The  stresses  in  a  portal  with  columns  fixed  may  be  calculated  by 
considering  the  columns  hinged  at  the  point  of  contra-flexure  and  solv- 
ing as  in  Case  I. 

Algebraic  Solution.  —  In  Fig.  61  we  have 


and          V  =  —  V1 


Having  found  the  reactions  H  and  H1,  V  and  V*,  the  stresses  in 
the  members  are  found  by  taking  moments  as  in  (a)  Fig.  58,  consider- 
ing the  columns  as  hinged  at  the  point  of  contra-flexure. 

The  shear  diagram  for  the  columns  is  as  shown  in  (a)  and  the  mo- 
ment diagram  as  in  (c)  Fig.  61. 

Anchorage  of  Columns.  —  In  order  that  the  columns  be  fixed,  the 
anchorage  of  each  column  must  be  capable  of  developing  a  resisting 

T  T     J 

moment  greater  than  the  overturning  moment  M  =  --  =—  ,  shown  in 


n6 


STRESSES  IN  PORTALS 


(c)  Fig.  61.  The  anchorage  required  on  the  windward  side  is  a  max- 
imum and  may  be  calculated  as  follows :  Let  T  be  the  tension  in  the 
windward  anchor  bolt,  20,  be  the  distance  center  to  center  of  anchor 


•±jcl 


IOOO 


6     -1000  F      -tJOOO          E.    R=2000 


96000  in-lbs-- 


H=|000 


Shear 
(a) 


Portal 

Columns  Fixed 

(b) 

PIG.  61. 


Moment 


(C) 


k-za  - 


Base  of  Column 

Id) 


bolts,  and  P  be  the  direct  load  on  the  column.    Taking  moments  about 
the  leeward  anchor  bolt  we  have 


2  Ta  — 


T_ 

" 


—  V)a  -f- 
Hd    ,P-V 


(58) 


If  the  nuts  on  the  anchor  bolts  are  not  screwed  down  tight,  there 
will  be  a  tendency  for  the  column  to  rotate  about  the  leeward  edge  of 
the  base  plate,  and  both  anchor  bolts  will  resist  overturning. 

The  maximum  pressure  on  the  masonry  will  occur  under  the 
leeward  edge  of  the  base  plate  and  will  be 

W    ,    Me 


COLUMNS  FIXISD,  GRAPHIC  SOLUTION 


117 


where  W  =  direct  stress  in  post; 

A    =  area  of  base  of  column  in  sq.  ins. ; 
M  =  bending  moment  =  ^  Hd; 
c    =  one-half  the  length  of  the  base  plate; 
/    =  moment  of  inertia  of  the  base  plate  about  an  axis  at  right 

angles  to  the  direction  of  the  wind. 

Graphic  Solution. — The  stresses  in  the  portal  in  Fig.  62  have  been 
calculated  by  graphic  resolution.  This  problem  is  solved  in  the  same 
manner  as  the  simple  portal  with  hinged  columns  in  Fig.  59. 


-1500  4-1000 


A 

ain-ai                   > 
/ 

/\          7\ 

?  •     T 

£. 

_.  

/ 

7  /o    v\      ^     /p  ^\.  3 

\ 

M 

/  fl 

2"\ 

m 

-¥= 

#-"" 

\ 

f                     \j                    \ 

--^ 

= 

+  1300*                -1300 

m 

loaooo 

rvlbs 

-  ~ 

v    9 
\ 

1 

1  / 

\EE 



b  \ 

«i                                                    « 

/                t 

^ 

\ 
\ 

!     I  d        ? 

/a    o 

'         V 

/ 

\ 

____ 

H'  J, 

Vo                        H 

= 

IOOO     1 

B                                  —  —  —  > 
<              -^                  looo    , 

fA         J: 

| 

= 

V 

V 

|t 

:1 

i 

***~~" 

==A 

= 

._i 

-X 

'-^=-108000.  nibs-  '»H  =  IOOO        fc^l                                                       VTA 

Moment 

Shear                              Fbrtal 

2 

1   9                           8 

<£  

\ 

•'?•••       "7        CASE    a 

V 
V 

/     \                                Columns  Fixed 

\ 

.               \ 

\ 
\ 

f         \         /               Stress    Diagram 

\         / 

\        /                        o        tooo     aooo     3000 

i   V 

••  JL'5       w             & 

1           '           f 

A 

\7 

s5        b             /7 

\                /          Compression    • 

\         /              Tension                       . 

FIG.  62. 

STRESSES  IN  CONTINUOUS  PORTALS.  —  The  portal 
with  five  bays  shown  in  Fig.  63  will  be  considered.  The  columns  will 
all  be  assumed  alike  and  the  deformation  of  the  framework  will  be 
neglected.  The  shears  in  the  columns  at  the  base  will  be  equal,  and  will 


u8 


STRESSES  IN  PORTALS 


be  H=  ^ 

To  find  the  vertical  reactions  proceed  as  follows:  Determine  the 
center  of  gravity  of  the  columns  by  taking  moments  about  the  base  of 
one  of  the  columns.  Now  there  will  be  tension  in  each  one  of  the 
columns  on  the  windward  side  and  compression  in  each  one  of  the 
columns  on  the  leeward  side  of  the  center  of  gravity  of  the  columns. 
The  sum  of  the  moments  of  the  reactions  must  be  equal  to  the  moment 


XX 

XX 

XX 

XX 

XX 

1 

h 

*""\ 

Va  ^ 
--  d&  

CG-of  Posts 
V*  \  ti* 

—  .  dl  -- 

H» 

...  : 
V, 

FIG.  63. 

of  the  external  wind  load,  R.  The  reactions  at  the  bases  of  the  columns 
will  vary  as  the  distance  from  the  center  of  gravity  and  their  moments 
will  vary  as  the  square  of  the  distance  from  the  center  of  gravity.  Now, 
if  a  equals  the  reaction  of  a  column  at  a  units  distance  from  the  center 
of  gravity,  we  will  have  V±  =  —  a  dlt  Vz  =  —  a  d2,  Vz  --  —  a  dzt 
Vi  =  +  a  dt,  F5  =  +  a  d5,  and  FQ  =  '+  a  dQ 
and  the  moment 

M  =  a    d,*      d*  +  d>*  +  d?      V      rf2    =Rh 


a         -  = 


(59> 


Having  found  a,  the  vertical  reactions  may  be  found. 

Now  having  found  the  external  forces  H  and  V,  the  stresses  can 
be  calculated  by  either  algebraic  or  graphic  methods. 

Stresses  in  a  Double  Portal.  —  To  illustrate  the  general  problem 
the  stresses  in  a  double  portal  are  calculated  by  graphic  resolution  in 
Fig.  64.  In  this  case 


DOUBLE  PORTAL 


119 


and 


=  //=11_=  1000  Ibs. 


V  =  —  F1  =       L  =  2250  Ibs. 


The  vertical  reaction  of  the  middle  column  is  zero.  By  substitut- 
ing the  dotted  members  as  shown,  the  stresses  can  be  calculated  as  in  the 
case  of  the  simple  portal.  The  full  lines  represent  stresses  in  the  portal 
members.  The  shear  in  the  columns  is  equal  and  is  H  below,  and 


H  d 
h-d 


above  the  foot  of  the  knee  brace. 


+  I75O 


-f-  I2OO 


+57OO 


R=30OO 


CASE  I 

Columns  Hinged 

Stress  Diagram 

0        1000   2000    3000 


Compression 
Tension 


FIG.  64. 

The  maximum  bending  moment  occurs  at  the  foot  of  the  knee 
brace  and  is 

M  =  H  d  =  192,000  inch-lbs. 


CHAPTER  XIII. 
STRESSES  IN  THREE-HINGED  ARCH. 

Introduction. — An  arch  is  a  structure  in  which  the  reactions  are 
inclined  for  vertical  loads.  Arches  are  divided,  according  to  the  num- 
ber of  hinges,  into  three-hinged  arches,  two-hinged  arches,  one-hinged 
arches,  and  arches  without  hinges  or  continuous  arches.  Three-hinged 
arches  are  in  common  use  for  exposition  buildings,  train  sheds  and  other 
similar  structures.  Two-hinged  arches  are  rarely  used  in  this  country ; 
continuous  arches  are  used  only  in  dome  construction. 

A  three-hinged  arch  is  made  up  of  two  simple  beams  or  trusses. 
Trussed  three-hinged  arches,  only,  will  be  considered  in  this  chapter, 
and  trussed  two-hinged  arches  in  the  next. 

CALCULATION  OF  STRESSES.— The  reactions  for  a  three- 
hinged  arch  can  be  calculated  by  means  of  simple  statics  with  slightly 
more  work  than  that  necessary  to  obtain  the  reactions  in  simple  trusses. 
Having  determined  the  reactions  the  stresses  may  be  calculated  by  the 
ordinary  algebraic  and  graphic  methods  used  in  the  solution  of  the 
stresses  in  simple  roof  trusses. 

Calculation  of  Reactions:  Algebraic  Method. — Let  H  and  V, 
H1  and  F1  be  the  horizontal  and  vertical  reactions  at  the  left  and  right 
supports  for  a  concentrated  load  P,  placed  at  a  distance  x  from  the 
center  hinge  C  in  the  three-hinged  arch  in  Fig.  65. 

From  the  three  fundamental  equations  of  equilibrium 

S  horizontal     components    of    forces  =  o  (a) 

S  vertical   components  of  forces  =  O  (b) 

S  moments  of  forces  about  any  point  =  O  (c) 


CALCULATION  OF  REACTIONS 


121 


FIG.  65. 

we  have  H  =  H1 

and  V  +  V*  —  P 

Taking  moments  about  B,  we  have 


and  taking  moments  about  center  hinge  C,  we  have 

T" 
Solving  (60)  we  have 


and  y1  ~  P —  V '=  . 

Substituting  (61)  in  (62),  we  have 

r  r          m          •t 


(60) 
(61) 

(62) 
(63) 

(64) 


The  horizontal  reactions  at  the  crown  are  the  same  as  at  the  sup- 
ports. Reactions  for  an  inclined  load  may  be  found  by  substituting  the 
proper  moment  arms. 

Calculation  of  Reactions :  Graphic  Method. — Let  P,  Fig.  66,  be 
the  resultant  of  all  the  loads  on  the  left  segment.  Since  there  is  no 


122 


STRESSES  IN    THREE-HINGED  ARCH 


bending  moment  at  hinge  C,  the  line  of  action  of  the  reaction  R2  must 
pass  through  the  hinge  at  the  crown.  This  determines  the  direction  of 
reaction  R2,  and  since  the  three  external  forces  R±,  R2  and  P  produce 
equilibrium  in  the  structure  they  must  meet  in  a  point.  Therefore  to 
find  the  direction  of  Rt  produce  B  C  to  d  and  join  d  and  A. 


FIG.  66. 


The  values  of  R^  and  R2  may  then  be  obtained  from  the  force  poly- 


gon. 


The  reactions  due  to  loads  on  the  right  segment  may  be  found  in 
the  same  manner.  The  two  operations  may  be  combined  in  one  as  il- 
lustrated in  the  solution  of  the  dead  load  stresses  in  a  three-hinged  arch, 
Fig.  67. 

Calculation  of  Dead  Load  Stresses. — To  find  the  reactions  for 
the  dead  loads  in  Fig.  67,  the  loads  are  laid  off  on  the  load  line  of  the 
force  polygon  in  order,  beginning  at  the  left  reaction  A,  and  two  equi- 
librium polygons,  one  for  each  segment,  are  drawn  using  the  same 
force  polygon.  The  vertical  reactions  at  the  crown,  PQ  ,  and  at  abut- 
ments, PR  and  />Bt  are  found  by  drawing  a  line  through  pole  o  of  the 
force  polygon  parallel  to  the  closing  lines  of  the  equilibrium  polygons. 
The  load  PQ  at  the  crown  causes  reactions  R^  and  RJ,  and  combining 


DEAD  LOAD  STRESSES 


I23 


reactions  R^  and  PR   at  A,  and  RS  and  PB  at  5,  we  have  the  true 
reactions  7^  and  R2. 


Stress  Diagram  Force  Polygon 


FIG.  67. 

Having  obtained  the  reactions,  the  stresses  in  the  members  are 
found  in  the  same  manner  as  in  simple  trusses.    In  Fig.  67  the  stresses 

in  the  left  segment  are  calculated  by  graphic  resolution.    The  diagram 
10 


I24 


STRESSES  IN  THREE-HINGED  ARCH 


is  begun  with  the  left  reaction  x-y  =  Rt.    Where  the  dead  load  is  sym- 
metrical a  stress  diagram  need  only  be  drawn  for  one  segment. 


WIND  LOAD 
STRESS  DIAGRAM 

FOR 

WINDWARD  51  DEL 


12 


FIG.  68. 


WIND  LOAD  STRESSES 


I25 


Calculation  of  Wind  Load  Stresses. — The  reactions  for  wind 
load  in  Fig.  68  are  found  as  follows : 

The  reactions  Pa  and  P c  for  the  windward  segment,  considering 
it  a  simple  truss  supported  at  the  hinges,  are  found  by  means  of  force 


13 


WIND  LOAD 
STRESS    DIAGRAM 

FOR 
LEEWARD  SIDE 


0         1000     2000    3000  4000 
I i i | i 


10 


FIG.  69. 


i26  STRESSES  IN  THREE-HINGED  ARCH 

and  equilibrium  polygons.  The  lines  of  action  of  Pa  and  Pc  are  par- 
allel to  each  other  and  to  the  resultant  R.  The  line  of  action  of  the 
right  reaction,  R2,  must  pass  through  the  center  hinge  C,  and  the  reac- 
tion Fc  will  be  replaced  by  two  reactions  R2  and  R^  parallel  to  R^ 
and  Rj1  in  the  arch  respectively,  and  the  force  triangle  will  be  closed 
by  drawing  7^  in  the  force  polygon.  The  intersection  of  force  R  and 
reactions  R±  and  R2  falls  outside  the  limit  of  the  diagram. 

Having  obtained  the  reactions,  the  stresses  in  the  members  are 
calculated  in  the  same  manner  as  in  a  simple  truss. 

The  wind  load  stresses  must  be  calculated  in  both  the  windward 
and  leeward  segments.  The  wind  load  stress  diagram  for  the  wind- 
ward segment  is  shown  in  Fig.  68,  and  for  the  leeward  segment  in  Fig. 
69,  compression  being  indicated  in  the  stress  diagrams  by  heavy  lines 
and  tension  by  light  lines.  Both  wind  load  stress  diagrams  and  the  dead 
load  stress  diagram  are  usually  constructed  for  the  same  segment  of  the 
arch.  By  comparing  wind  load  stress  diagrams  in  Fig.  68  and  Fig.  69, 
it  will  be  seen  that  there  are  many  reversals  in  stress.  The  maximum 
.stresses  found  by  combining  the  dead,  snow  and  wind  load  stresses  as 
in  the  case  of  simple  trusses  and  transverse  bents,  are  used  in  designing 
Ihe  members. 


CHAPTER  XIV. 
STRESSES  IN  TWO-HINGED  ARCH. 

Introduction. — A  two-hinged  arch  is  a  frame-work  or  beam  with 
hinged  ends  which  has  inclined  reactions  for  vertical  loads.  The  bot- 
tom chords  of  two-hinged  arches  are  usually  cambered,  however,  a 
simple  truss  becomes  a  two-hinged  arch  if  the  ends  are  fixed  to  the 
abutments  so  that  deformation  in  the  direction  of  the  length  of  the 
truss  is  prevented. 

The  horizontal  components  of  the  reactions  may  be  supplied  either 
by  the  abutments  or  by  a  tie  connecting  the  hinges.  In  the  latter  case 
the  deformation  of  the  tie  must  be  considered  in  determining  the  hori- 
zontal reactions.  Two-hinged  arches  are  statically  indeterminate  struc- 
tures and  their  design  is  subject  to  the  same  uncertainties  as  continuous 
and  swing  bridges. 

Two-hinged  roof  arches  are  rigid  and  economical,  but  have  been 
used  to  a  very  limited  extent  on  account  of  the  difficulties  experienced 
in  their  design.  The  methods  outlined  in  this  chapter  are  quite  simple 
in  principle,  although  they  necessarily  require  quite  extended  calcula- 
tions. Two-hinged  roof  arches  with  open  framework,  only,  will  be 
considered  in  this  chapter. 

CALCULATION  OF  STRESSES.— The  vertical  reactions  in  a 
two-hinged  arch  are  the  same  as  in  a  simple  truss  or  a  three-hinged  arch 
having  the  same  loads  and  span.  The  horizontal  reactions,  however,  de- 
pend upon  the  deformation  of  the  framework  and  cannot  be  determined 
by  simple  statics  alone.  Before  the  deformations  can  be  calculated,  the 
sizes  of  the  members  must  be  known,  and  conversely,  before  the  sizes 


128 


STRESSES  IN  TWO-HINGED  ARCH 


of  the  members  can  be  calculated,  the  stresses  which  depend  upon  the 
deformations  must  be  known.  Any  method  for  the  calculation  of  the 
stresses  in  a  two-hinged  arch  is,  therefore,  necessarily  a  method  of 
successive  approximations.  With  a  skilled  computer,  however,  it  is 
rarely  necessary  to  make  more  than  two  or  three  trials  before  obtain- 
ing satisfactory  results  in  designing  roof  arches.  Two-hinged  bridge 
arches  require  somewhat  more  work  to  design  than  roof  arches  on 
account  of  the  greater  number  of  conditions  for  maximum  stresses  in 
the  members. 

Having  determined  the  correct  value  of  the  horizontal  thrust,  H, 
the  stresses  in  a  two-hinged  arch  may  be  calculated  by  the  ordinary 
algebraic  or  graphic  methods  used  in  the  solution  of  the  stresses  in 
simple  trusses. 

Calculation  of  the  Reactions. — In  Fig.  70  the  vertical  reactions, 
F!  and  F2,  are  the  same  as  for  a  simple  truss.  The  horizontal  reactions, 
H,  will  be  equal  and  will  be  the  forces  which  would  prevent  change  in 
length  of  span  if  the  ends  of  the  arch  were  free  to  move.  The  horizon- 
tal thrust,  H,  will  therefore  be  the  force  which,  applied  at  the  roller  end 
of  a  simple  truss,  will  prevent  deformation  and  make  the  truss  a  two- 
hinged  arch. 

An  expression  for  H  may  be  determined  as  follows:  In  Fig.  70 
assume  that  all  members  are  rigid  except  the  member  1-3',  which  is 
increased  in  -length  8,  under  the  action  of  the  external  load,  W .  The 


w 


w 


H 


FIG.  70. 


CALCULATION  OF  THE  REACTIONS  129 

movement  of  the  truss  A'  at  the  hinge  Z/0  will  then  be  due  to  the 
change  in  length,     8,  of  the  member  i-y. 

Let  hl  be  the  horizontal  reaction  necessary  to  bring  L10  back  to 
its  original  position,  and  let  U  h1  be  the  stress  in  the  member  i-y  due 
to  the  horizontal  thrust  hl.  Now  the  internal  work,  y2  8  h1  U,  in  short- 
ening the  member  i-y  to  its  original  length  will  be  equal  to  the  external 
work,  y2  h1  A',  required  to  bring  the  hinge  LJ-  back  to  its  original 
position, 

%  hl  A'  =  ^  S  A1  U 
and  A'  =  5  U  (65) 

PL 

but  5  =  - — -,  where  P  is  the  unit  stress  in  the  member  i-y  due  to  the 


external  load  W  ,  L  is  the  length  of  the  member  i-y,  and  £  is  the  mod- 
ulus of  elasticity  of  the  material  of  which  the  member  is  composed. 
Substituting  this  value  of  8  in  (65)  we  have 

(66) 


where  U  is  the  stress  in  i-y  due  to  a  load    ~-  ~  unity  at  L10 

Now  if  each  one  of  the  remaining  members  of  the  arch  is  assumed 
to  be  distorted  in  turn,  the  others  meanwhile  remaining  rigid,  the  dis- 
tortion in  each  case  at  I/10  will  be  represented  by  the  general  equation 
(66)  and  the  total  deformation,  A  ,  at  L10  will  be 


A  =3-  (67) 

Let  P1  h1  be  the  unit  stress  in  the  member  i-y  due  to  a  horizontal 
thrust  H1,  then  by  the  same  reasoning 

S  U  (65a) 

1  V  L 
but 


and 

and  the  total  deformation,  A,  will  be 


130  STRESSES  IN  TWO-HINGED  ARCH 

A1  Pl  U  L  .Pl  UL 


Now  for  equilibrium,  the  values  of  A  as  given  in  equations  (67) 
and  (68)  must  be  equal,  and  we  have,  after  solving  for  H 


(69) 

which  is  an  expression  for  computing  the  horizontal  thrust  in  any  two- 
hinged  arch  due  to  external  loads.  This  formula  holds  for  any  system 
of  loading  as  long  as  P  is  the  unit  stress  due  to  that  loading,  U  is  the 
stress  in  the  member  and  F1  is  the  unit  stress  in  the  member  due  to  a 
unit  load  acting  at  the  point  at  which  the  deformation  is  desired,  and 
parallel  to  the  direction  in  which  the  deformation  is  to  be  measured. 

The  method  of  finding  the  correct  value  of  the  horizontal  reaction, 
H,  is  as  follows:  (i)  calculate  the  stresses  in  the  arch  for  the  given 
loading  on  the  assumption  that  it  is  a  simple  truss  with  one  end  sup- 
ported on  frictionless  rollers;  (2)  calculate  the  stresses  in  the  arch  for 
'an  assumed  horizontal  reaction,  H1  — ,  say,  20000  Ibs.  on  the  assumption 
that  it  is  a  simple  truss  on  frictionless  rollers;  (3)  calculate  the  defor- 
mation, A,  of  the  free  end  of  the  truss  for  the  given  loads  by  means 
of  formula  (67)  ;  (4)  calculate  the  deformation,  A'  of  the  free  end  of 
the  truss  for  the  assumed  horizontal  reaction  H1  =  20000  Ibs.  by  means 
of  formula  (68).  The  true  value  of  H  is  then  by  formula  (69)  given 
by  the  proportion 

H\  H*  ::  A:  A' 

_  7/1  A          20000  A  (70) 

y/=    ~~A^          ~A^~~ 

The  calculation  of  the  horizontal  reaction,  H,  and  the  stresses  can 
be  made  by  algebraic  methods  alone  or  by  a  combination  of  graphic 
and  algebraic  methods.  The  first  requires  less  work,  while  the  second 


ALGEBRAIC  CALCULATION  OF  REACTIONS  T3T 

is  probably  easier  to  understand.  The  algebraic  solution  will  be  given 
first. 

Algebraic  Calculation  of  Reactions. — In  Table  VII  the  values 
of  the  unit  stress,  P,  in  each  member  due  to  the  external  loads  are  given 

P  L 

in  column  5 ;  values  of  — —  are  given  in  column  6 ;  values  of  the  stress, 

U ' ,  in  each  member  due  to  a  unit  horizontal  thrust  are  given  in  column 

P  U  L 

8 ;  and  values  of —  are  given  in  column  9.    The  algebraic  sum  of 

h. 

the  quantities  in  column  9  gives  the  total  deformation,  A  =  .956 
inches  at  the  point  where  the  unit  horizontal  thrust  was  applied  meas- 
ured parallel  to  the  line  of  action  of  the  thrust. 


TABLE  VII. 


Simple  Truss  with  Vertical  Loads 


1 

Member 

2 

Area 
Sq-in- 

3 

Lenqth,L 
inches 

4 

Stress 
Ibs- 

5 

UnitStress 
P  Ibs- 

6 
PL 

E 

7 

No-  of 
Mem- 

8 
U 

9 
PUL 
| 

i-x 

5-3 

252 

+6000O 

+  //32O 

+.095 

9 

-0-90 

-•086 

2-X 

5-5 

/9^ 

f4/OOO 

+  7740 

+•050 

6 

-0-80 

-•O40 

4-X 

53 

180 

1-67000 

-1-12650 

+•076 

1 

-1-45 

-110 

2'-X 

53 

/92 

±41000 

+  7740 

+•050 

12 

-0-80 

-•040 

r-x 

5-3 

252 

i-60000 

+//320 

+•095 

15 

-O-90 

--O86 

I-Y 

5-3 

216 

-250OO 

-  472O 

-•034 

8 

+/-60 

-•O54- 

3-Y 

5-3 

192 

-57000 

-/O760 

-•069 

4- 

+2-05 

-•141 

3LY 

53 

192 

-57000 

-IO760 

-•069 

IO 

+2-05 

-•141 

I-Y 

53 

216 

-25OOO 

-  4720 

-•034 

14 

+1-60 

-•054 

1-2 

20 

150 

-30000 

-/50OO 

-075 

7 

+075 

-•056 

2-3 

4-0 

204 

+32000 

+  80OO 

+•054 

5 

-0-45 

-•024 

3-4 

4-0  < 

150 

-22000 

-  5500 

-02d 

2 

+0-80 

-O22 

3L  4 

40' 

150 

-22000 

-  5500 

-•028 

3 

+0-QO 

-•022 

2  '-3' 

4-0 

204- 

+32000 

-h  6000 

+  •054- 

II 

-0-45 

-•024 

l'-2' 

2-0 

150 

-30OOO 

-/5000 

-•075 

13 

-+075 

-056 

Total  Deformation  =i£Uk=    -956 

In  Table  VIII  similar  values  are  given  for  the  arch  as  a  truss 
with  an  assumed  horizontal  reaction  of  J/1  =  20000  Ihs.  The  algebraic 
sum  of  the  quantities  in  column  9  gives  the  total  deformation,  A'  r= 
.5/4  inches  at  the  point  where  the  horizontal  thrust  was  applied. 


STRESSES  IN  TWO-HINGED  ARCH 


TABLE  VIII. 


Simple  Truss  with  H  =20000  Ibs. 


Member 

2 

Area 
Sq-in- 

3 

LengthJ- 
inches 

4 

Stress 
Ibs. 

5 

(Jnit.Stress 
P  Ibs. 

P! 

7 

No-of 
Mem- 

8 
U 

,9 

PUL 

E 

I-X 

53 

252 

-18000 

-34OO 

-*028 

9 

-0-90 

.025 

2-X 

53 

192 

-/6000 

-3000 

-0/9 

6 

-0-80 

•015 

4-X 

53 

160 

-29000 

-  5500 

-•033 

I 

-1-45 

•048 

Z'-X 

53 

/92 

-16000 

-3000 

-019 

IZ 

-0-80 

•0/5 

I'-X 

53 

252 

-18000 

-3400 

-•028 

15 

-0-90 

.025 

I-Y 

53 

216 

+32000 

+  6000 

+•043 

'  8 

+160 

•069 

3-Y 

53 

192 

+41000 

+  7800 

+•050 

4 

+2-05 

.102 

3'Y 

53 

192 

+41000 

+  7800 

+  050 

10 

+205 

.102 

I'-Y. 

53 

216 

+32000 

+  6000 

+043 

14 

+/-60 

•069 

1-2  * 

2-0 

/50 

+15000 

+  7500 

+•038 

7 

+075 

.029 

2-3 

4.0 

204 

-9000 

-2250 

-•015 

5 

-0-45 

.007 

3-4, 

40 

/50 

+16000 

+  4000 

+-020 

2 

+0-80 

.016 

3~4 

4.0 

150 

+/6000 

+4000 

+•020 

3 

+0-60 

•016 

2-3; 

40 

204 

-9000 

-2250 

-.015 

II 

-0-45 

•007 

20 

/50 

+15000 

+  7500 

+.038 

13 

+075 

•029 

Total  Deformation  =  2  P'UL-  .574 

TABLE  IX. 


Simple  Truss  with  Dead  and  Wind  Loads 


1 
Member 

2 
Area 
Sq.in- 

3 
Lenqtht 
inches 

4 

Stress 
Ibs. 

5 

Unit  Stress 
Plbs. 

6 
PL 

E 

7 

No-of 
Mem- 

Q 
U 

9 

E 

I-X 

53 

252 

+870OO 

+/640O 

+138 

9 

-030 

-.124 

2-X 

5-3 

/9Z 

+72OOO 

+/36OO 

+•087 

6 

-0-80 

-•069 

4-X 

5-3 

180 

+95000 

+/78OO 

+107 

I 

-1.45 

-•155 

2'-X 

5-3 

/92 

+52OOO 

+  9600 

+•063 

12 

-0-80 

-050 

I'-X 

5-3 

252 

+72000 

+/3600 

+114 

15 

-090 

-•/03 

I*Y 

5-3 

216 

-58000 

-/0900 

-.078 

6 

+/-60 

-.125 

3-Y 

53 

/92 

-87OOO 

-16400 

-105 

4 

+2-05 

-.2/5 

3-Y 

53 

/92 

-74OOO 

-I4OOO 

-.090 

10 

+2-05 

-.185 

I'-Y 

5-3 

2/6 

-30000 

-5650 

-.041 

fl 

+/-60 

-.064 

1-2 

2.0 

/50 

-360OO 

-/80OO 

-.090 

7 

+0,75 

-.067 

2-3 

40 

204 

+28000 

+  70OO 

+-048 

5 

-0.45 

-JD2Z 

3-4 

4-0 

/50 

-22000 

-5500 

--028 

2 

+0-80 

-.022 

3-4 

4.O 

150 

-42OOO 

-/0500 

-053 

3 

+0-80 

-.042 

2'-3' 

4.0 

204 

+46000 

+II5OO 

+O78 

II 

-0.45 

-.035 

l'-2' 

2-0 

/50 

-420OO 

-2/000 

--I05 

13 

+075 

-.079 

Total  Deformation  =2^=^-=  1357 

GRAPHIC  CALCULATION  OF  REACTIONS 


'33 


The  correct  value  of  H  is  given  by  the  proportion 

H  \  H1  ::  A  :  A' 
20000  X  .956 


.574 


=  33400  Ibs. 


In  Table  IX  the  deformation,  A,  for  the  same  arch  considered  as 
a  simple  truss  and  acted  upon  by  dead  and  wind  loads  is  1 . 357  inches, 
and 

20000  X  1.357 


H 


.574 


=  47300  Ibs. 


Graphic  Calculation  of  Reactions. — In  the  graphic  solution  of 
the  horizontal  reactions  the  total  amount  of  the  deformations,  A  and   A 
are     found    by     means     of    deformation     diagrams.       Before     con- 
structing   the     deformation    diagrams    the    quantities    in    the    first 
seven  columns  in  Tables  VII  and  VIII    or    VIII    and    IX  must  be 


Simple  Truss 

Vertical  Loads 

(a) 


Simple  Truss 
(b) 


-o- 


Simple  Truss^ 
H =20000  Ibs. 

(C) 


H«£0000lbs. 
Y 


Stress  Diagram,  H=20000lbsi 
(d) 


FIG.  71. 


i34  STRESSES  IN  TWO-HINGED  ARCH 

calculated.  The  stresses  given  in  column  4  are  calculated  as  shown 
in  Fig.  71.  Column  6,  giving  deformations  of  each  member,  and  col- 
umn 7,  giving  the  order  in  which  these  deformations  are  used,  are,  how- 
ever, the  only  values  used  in  constructing  the  deformation  diagrams. 

Deformation  Diagram. — The  principle  upon  which  the  construc- 
tion of  the  deformation  diagram  is  based  is  as  follows :  Take  the  two 
members  a-c  and  c-b  in  (d)  Fig.  72,  meeting  at  the  point  c.  Assume 
that  a-c  is  shortened  and  b-c  is  lengthened  the  amounts  indicated.  It 
is  required  to  find  the  new  position,  c'y  of  the  point  c.  With  center  at  a 
and  a  radius  equal  to  the  new  length  of  a-c  =  a-c',  describe  an  arc. 
The  new  position  of  c  must  be  some  place  on  this  arc.  Then  with  a 
center  at  b  and  a  radius  equal  to  the  new.  length  of  b-c  =  b-c',  describe 
an  arc  cutting  the  first  arc  in  c'.  The  new  position  of  c  must  be  some 
place  on  this  arc  and  will  therefore  be  at  the  intersection  of  the  two 
arcs,  c'.  Since  the  deformations  of  the  members  are  always  very  small 
as  compared  with  the  lengths  of  the  members,  the  arcs  may  be  replaced 
by  perpendiculars,  and  the  members  themselves  need  not  be  drawn,  (e) 
Fig.  72. 

To  draw  the  deformation  diagram,  (b)  Fig.  72,  for  the  arch 
as  a  truss  with  one  end  on  frictionless  rollers  and  loaded  with  vertical 
loads,  proceed  as  follows :  Begin  with  the  member  marked  I,  lay  off  its 
deformation  =  +  .076  inches  (Table  VII.,  column  6)  to  scale  and 
parallel  to  member  I.  Now  lay  off  the  deformation  of  2  =  —  .028 
inches  away,  from  the  joint  U2  and  parallel  to  the  member  2,  and  lay 
off  deformation  of  3  =  —  .028  inches,  away  from  the  joint  U'2  and 
parallel  to  the  member  3.  Perpendiculars  erected  at  the  ends  of  de- 
formations 2  and  3  will  meet  in  the  new  position  of  L2.  The  vertical 
distance  between  the  deformation  I  and  point  L2  represents  to  scale  the 
change  in  position  of  L2  relative  to  the  member  U2  t/V  At  L2  in  the 
deformation  diagram  lay  off  deformation  of  4  =  —  .069  inches,  away 
from  the  joint  and  parallel  to  the  member  4,  and  at  U2  lay  off  deforma- 
tion of  5  =  +  .054  inches,  toward  the  joint  and  parallel  to  the  member 
5.  The  perpendiculars  erected  at  the  ends  of  the  deformations  4  and  5 


DEFORMATION  DIAGRAM 

v? 


'35 


0.9 5 6  inches  —  -  -  j-j-j-j-j-j-  ~~zi rrri 

O"          0.1"        0£~        G3"        "'"  -'"'  Lo 


Deformation  Diagram 

for 

Simple  Truss 


(b) 


v 


s>  ^./         \* Of  /  %  y 

-.     ,  r^  /"^       ^'\         /  /  I5\  £9  \ 

Deformation  Diagram   /^>%\   /  /          .--''      *^^  \ 

for  \u^!  .    ^/  ,    x'l^-''''  ^-Ox 


Simple  Truss 
Vertical  Loads 


« 0.574  inches 

FIG.  72. 


.-.-.vfa'-( 


determine  the  new  position  of  joint  Z,t  relative  to  the  other  points.  In 
like  manner  perpendiculars  erected  at  the  ends  of  deformations  6  and 
7  determine  Ulf  and  finally  perpendiculars  erected  at  the  ends  of 
deformations  8  and  9  determine  L0.  The  deformation  diagram  for  the 
right  half  of  the  truss  is  constructed  in  the  same  manner.  The  horizon- 
tal line  joining  Z<0  and  Z/0  represents  to  scale  the  movement  of  the 
joint  L10. 

In  drawing  the  deformation  diagram  it  is  immaterial  whether  plus 
deformations  are  laid  off  toward  the  joints  and  minus  deformations 
away  from  the  joints  as  was  done  in  the  preceding  problem,  or  the 
reverse.  The  former  method  is  more  common,  but  the  latter  is  prob- 
ably more  consistent.  The  deformation  diagram  (&.)  if  drawn  in  the 
latter  way  would  be  turned  upside  down  and  inside  out. 

Calculation  of  Dead  Load  Stresses  in  Arch. — In  Fig.  71,  (b) 
is  the  stress  diagram  for  the  arch  as  a  simple  truss  with  vertical  loads 
as  shown  in  (a)  ;  and  (d)  is  the  stress  diagram  for  the  arch  as  a  simple 


136 


STRESSES  IN  TWO-HINGED  ARCH 


truss  with  a  horizontal  thrust,  H1,  of  20000  Ibs.  as  shown  in  (c).  The 
quantities  for  calculating  the  deformations  of  the  simple  truss  with 
vertical  loads  are  given  in  Table  VII,  and  the  deformation  diagram 
is  shown  in  (fr)  Fig.  72.  The  quantities  for  calculating  the  deforma- 
tions of  the  simple  truss  with  a  horizontal  thrust  of  20000  Ibs.  are  given 
in  Table  VIII,  and  the  deformation  diagram  is  shown  in  (c)  Fig.  72. 
The  true  value  of  H  is  found  by  the  proportion 

H  :  20000  :  :  .956  :  .574 
H  =  33400  Ibs. 

The  stress  diagram  for  the  two-hinged  arch  with  V  =  V  =  42000 
Ibs.,  and  H  =  H  =  33400  Ibs.  is  shown  in  (b)  Fig.  73. 

The  difference  in  the  stresses  in  the  members  of  a  simple  truss 
and  a  two-hinged  arch  may  be  seen  by  comparing  stress  diagram  (&) 
Fig.  71,  and  stress  diagram  (b)  Fig.  73,  both  diagrams  being  drawn 


20000        40000 


Two  Hinged  Arch 
(a) 


FIG.  73. 


Stress  Diagram 

Two  Hinged  Arch 

(b) 


to  the  same  scale.  The  stresses  in  the  arch  may  be  found  from  the 
stresses  given  in  Tables  VII  and  VIII  by  adding  the  stresses  in  column 
4,  Table  VII,  to  the  corresponding  stresses  in  column  4, 
Table  VIII,  multiplied  by  1 . 67,  the  ratio  between  the  actual  and  as- 


DEAD  AND  WIND  LOAD  STRESSES 


sumed  horizontal  reactions.  For  example,  the  stress  in  \-x  in  the  arch 
equals  +  60000  —  18000  x  i  .67  =  +  29800  Ibs.  Stress  in  1-3;  equals 
—  25000  +  32000  x  i  .  67  =  +  28440  Ibs. 

Dead  and  Wind  Load  Stresses  in  Arch.  —  In  Fig.  74,  (&)  is  the 
stress  diagram  for  the  arch  as  a  simple  truss  loaded  with  dead  and  wind 
loads  as  shown  in  (a).  Table  IX  gives  the  same  data  for  this  case  as 


o1       io* 


Simple  Truss 
Dead  and  Wind  Loads 

(a) 


Simple  Truss 
Dead  and  Wind  Load  Stress  Diaqrar 
(b) 


*$x 


u! 


o         aoooo     40000 


Simple  Truss 

H- 20000  Ibs. 

(c) 


FIG.  74. 


Stress  Diagram  ,  H -20000  Ibs. 
(d) 


are  given  in  Table  VII  for  the  simple  truss  with  vertical  loads.  The 
deformation  diagram  for  the  deformations  given  in  column  6,  Table 
IX,  is  shown  in  (b)  Fig.  75.  In  drawing  the  deformation  diagram  for 
this  case  the  member  marked  i  was  assumed  to  be  fixed  in  position  and 
the  other  members  were  assumed  free  to  move.  The  horizontal  dis- 
tance between  L0  and  Z/0  will  be  the  total  deformation  required. 


STRESSES  IN  TWO-HINGED  ARCH 

1-357  inches 


N 
\ 

\ 


U2  U2  >^  .-'"  / 

>^;     ^  ^""" 

0"        O-l"      0-2"      03"      04" 


m^j  w 

/        ufcVu        \  \       r><:      V    Defo 

/  ^rV^»  \      v<-  ^LlW 

/  --  "^^\          *  iib^-1— ^TIJ, 


Deformation  Diagram 

for 

=*u       v,r»      ---'         Simple  Truss 
0.374  inches •  \    X    ,'    /       Dead  and  Wind  Loads 


Deformation   Diagram 

for 

Simple  Truss 

H=  20000  Ibs, 

(C) 

FIG.  75. 


The  deformation  diagram  for  the  simple  truss  with  a  horizontal 
thrust,  H1,  of  20000  Ibs.  is  given  in  (c)  Fig.  75  and  is  the  same  as  that 
given  in  (c)  Fig.  72. 

The  true  value  of  H  is  found  by  the  proportion 
H  :  20000  :  :  1.357  '  -574 
H  =  47300  Ibs. 

The  stress  diagram  for  the  two-hinged  arch  with  dead  and  wind 
loads  and  a  horizontal  thrust,  H,  of  47300  Ibs.  is  given  in  (b)  Fig.  76. 
The  stresses  in  the  arch  for  this  case  may  be  found  from  the  stresses 
in  Tables  IX  and  VIII  by  adding  the  stresses  in  column  4,  Table  IX, 
to  the  corresponding  stresses  in  column  4,  Table  VIII,  multiplied  by 
2.865,  tne  ratio  between  the  actual  and  assumed  horizontal  reactions. 


ARCH  WITH  HORIZONTAL 


10*         20'        30' 


Two  Hinged  Arch 
(a) 


20000      40000 


Stress  Diagram 
Two  Hinged  Arch 
Cb) 

FIG.  76. 

As  a  check  on  the  accuracy  of  the  calculations  the  movement  at  L0' 
in  the  arch  was  calculated  in  Table  X  and  was  found  to  be  zero  as  it 
should  be. 

Arch  With  Horizontal  Tie. — If  a  horizontal  tie  is  used  the 
final  deformation  of  the  arch  will  be  equal  to  the  deformation  of  the  tie. 

TABLE  X. 

Two  Hinged  Arch  with  Dead  and  Wind  Loads 


1 

Member 

2 
Area 
5q-in- 

3 

Length,L 
inches 

4- 

Stress 
Ibs- 

5 
UnitStress 
P  Ibs- 

6 

* 

8 
U 

9 

¥• 

i-x 

53 

252 

+435OO 

+  Q220 

+.069 

-0-90 

-.063 

2-x 

55 

192 

+34200 

+  6450 

+•041 

-O.QO 

-'033 

4-X 

5-5 

180 

+26500 

+5000 

+.030 

-1.45 

-045 

2Lx 

5-5 

191 

+14200 

+2660 

+•017 

-0.80 

-.014 

r-x 

53 

252 

+29500 

+5550 

+.047 

-0.90 

--042 

I-Y 

5-5 

216 

+/80OO 

+3400 

+324 

+  1-60 

+.058 

3-Y 

5-5 

192 

+10000 

+  1890 

+•012 

+2-05 

+.025 

3LY 

5-5 

192 

+25000 

+4550 

+.028 

+2-05 

+.057 

I'-Y 

5-3 

216 

+46000 

+  8700 

+.062 

+/-60 

+.093 

1-2 

2-0 

150 

-    500 

-  250 

-.001 

+0.75 

-.001 

2-3 

4-0 

204 

+  6500 

+  1625 

+•011 

-0-45 

-.005 

3-4 

40 

150 

+I5QOO 

+5950 

+.020 

+0-80 

+.016 

3-4 

4-0 

150 

-4200 

-/05O 

-.005 

+0-80 

-.004 

2'-3' 

4.0 

204 

+22600 

-+5  7  00 

+.039 

-0-45 

-.018 

r-21 

20 

150 

-5000 

-2500 

-.013 

+075 

-.0/0 

Total  Deformation  =^EUL=.ooo 

II 


14°  STRESSES  IN  TWO-HINGED  ARCH 

Assume  that  the  joints  Z,0  and  L0r  in  (a)  Fig.  73  are  connected  by 
a  tie  having  3  sq.  in.  cross-section.  A  force  of  1000  Ibs.  will  stretch 
the  tie 

1000  X  720" 
=  3X  29,000.000  -  -0083  inches. 

574 
The  movement  for  1000  Ibs.  applied  as  H  is  equal  to  ^—  —  =  .0287 

inches.    The  value  of  H  therefore  which  will  produce  equilibrium  for 
the  arch  with  vertical  loads  will  be 

+  .0083  H  +  .0287  H  =  .956  x  looo  Ibs. 


The  stresses  in  the  arch  for  this  case  may  be  found  from  the  stresses 
in  Table  VII  and  Table  VIII  as  previously  described. 

Temperature  Stresses.  —  Where  a  horizontal  tie  is  used  and  all 
parts  of  the  structure  are  exposed  to  the  same  conditions  and  range  of 
temperature,  the  entire  arch  will  contract  and  expand  freely  and  tem- 
perature stresses  will  not  enter  into  the  calculations.  Where  the  tie  is 
protected  and  where  rigid  abutments  are  used  the  temperature  stresses 
must  receive  careful  attention. 

The  deformation  A'  due  to  a  uniform  change  of  temperature  of  t 
degrees  Fahr.  when  the  arch  is  assumed  to  be  a  truss  supported  on 
frictionless  rollers,  will  be  etL,  where  e  is  the  coefficient  of  expansion 
of  steel  per  degree  Fahr.  =  .  00000665  ;  t  equals  change  in  temperature 
in  degrees  Fahr.  ;  and  L  equals  the  length  of  the  span. 

For  a  change  of  75  degrees  Fahr.  from  the  mean,  the  deformation 
will  IDC 

A'  =  ±  .  00000665  X  75  L 

•=  ±      L 
2000 


DESIGN  OF  TWO-HINGED  ARCH  141 

For  the  arch  in  Fig.  73 

720" 
A'  =  rt    2000  —  ^  -36  inches 

<3/- 

This  will  be  equivalent  to  a  change  in  H  of  ±  -^=7    x  20000  =    ± 

12540  Ibs.  The  stresses  due  to  temperature  in  the  two-hinged  arch 
will  be  equal  to  the  stresses  in  column  4,  Table  VIII,  multiplied  by  =h 
.627.  The  maximum  stresses  due  to  external  loads  and  temperature 
will  be  found  by  adding  algebraically  the  temperature  stresses  to  the 
stresses  due  to  the  external  loads.  If  the  arch  is  not  erected  at  a  mean 
temperature  this  fact  must  be  taken  into  account  in  setting  the  pedestals. 

Design  of  Two-Hinged  Arch. — In  designing  a  two-hinged  roof 
arch  proceed  as  follows:  (i)  With  one  end  free  to  move,  calculate 
the  stresses  in  the  arch  as  a  simple  truss  5(2)  with  an  assumed  horizon- 
tal reaction,  H1,  of,  say,  20000  Ibs.,  calculate  the  stresses  in  the  arch  as 
a  simple  truss ;  (3)  calculate  the  stresses  in  the  arch  for  some  assumed 
value  of  H,  this  value  of  H  may  be  guessed  at  or  often  may  be  estimated 
with  considerable  accuracy  ;*  (4)  design  the  members  for  approximate 
stresses  in  the  arch  5(5)  calculate  the  deformation  of  the  arch  as  a  truss 
for  the  approximate  sections  and  stresses ;  (6)  calculate  the  deforma- 
tion of  the  arch  as  a  truss  for  an  assumed  horizontal  reaction  of  20000 
Ibs. ;  (7)  determine  a  more  accurate  value  of  H  from  the  deformations 
as  previously  described ;  (8)  recalculate  the  stresses  m  the  arch,  re- 
design the  members,  recalculate  the  deformations,  recalculate  a  new 
value  of  H,  etc.,  until  satisfactory  sections  are  obtained.  The  second 
approximation  is  usually  sufficient.  Corrections  for  horizontal  tie  and 
temperature  should  be  applied  in  making  the  approximations.  The 
gross  area  of  the  sections  of  all  members  should  be  used  in  determining 
the  deformation  of  the  members.  If  riveted  tension  members  are  much 
weakened,  a  somewhat  smaller  value  of  H,  say,  26,000,000,  may  be 
used  than  the  29,000,000  commonly  used  for  the  compression  members. 

The  method  just  described  is  much  more  expeditious  than  the 
usual  method  of  designing  the  members  for  the  stresses  found  by  con- 

*  See  note,  page  142. 


142  STRESSES  IN  TWO-HINGED  ARCH 

sidering  the  arch  a  simple  truss  with  allowable  stresses,  say,  twice 
those  to  be  finally  allowed.  In  the  latter  case  the  first  approximation  is 
usually  worthless  on  account  of  the  reversal  of  stresses  in  the  members 
which  have  been  designed  as  tension  members.  If  the  value  of  H  in  the 
first  method  is  taken  large  enough  to  make  members  in  compression 
that  the  designer's  judgment  or  experience  says  should  be  in  compres- 
sion, the  second  approximation  is  usually  final. 


.  —  As  a  first  approximation  assume  that  all  members  have  a  unit  area 
and  that  £  is  a  constant.    Then 

Go.) 


where  6"  =  total  stress  in  each  member  due  to  external  loads  ; 

U  =  stress  in  each  member  due  to  a  load  of  i  Ib.  acting  in  line  with  the 

horizontal  reaction  //. 

For  the  two-hinged  arch  carrying  dead  loads  from  Table  VIII  and  Table  IX, 
the  approximate  value  of  H  as  found  by  substituting  in  (7oa)  is,  H  —  33,000  Ibs., 
which  checks  the  true  value  very  closely. 


CHAPTER  XV. 


COMBINED  AND  ECCENTRIC  STRESSES. 

Combined  Direct  and  Cross  Bending  Stresses.  —  Thus 
far  members  of  trusses  and  frameworks  have  been  considered  as 
acted  on  by  direct  forces,  parallel  to  the  axis  of  the  member.  While 
this  is  the  more  common  case,  it  often  becomes  necessary  to  design 
members  which  support  loads  as  in  (a),  (b),  (c),  or  (d),  Fig.  77,  or  in 
which  the  line  of  action  of  the  external  force  does  not  coincide  with  the 
neutral  axis  of  the  member,  (e),  (f),  (g),  or  (h),  Fig.  77. 


FIG.  77- 


144      •  COMBINED  AND  ECCENTRIC  STRESSES 

The  following  nomenclature  will  be  used: 

Let  P  =  total  direct  loading  on  member  in  pounds  ; 

/    =  length  of  member  in  inches  ; 

L  =  length  of  member  in  feet; 

/    •=.  moment  of  inertia   of   member  ; 

y^  —  distance  from  neutral  axis  to  remote  fibre  on  side  for 
which  stress  is  desired; 

£  =  modulus  of  elasticity  of  the  material; 

e     =  eccentricity  of  P,  i.e.  distance  from  line  of  action  of 
P  to  neutral  axis  of  member  in  inches  ; 

v    =  deflection  of  member  in  inches; 

A  =  area  of  member  in  square  inches  ; 

ft    —  fibre  stress  due  to  cross  bending; 

r> 

/2  =  —  =  direct  fibre  stress  ; 
si 

M  =  total  bending  moment; 
M2  =  bending  moment  due  to  deflection,  =  P  v; 
MI  =  bending  moment  due  to  external  forces  and  is  equal  to 
Y^Wlm  (a)  and  (b)  ;  %  iv  I-  in  (c)  and  (d)  ;  and  P  e 
in  (e),  (f),  (g)  and  (h)  Fig.  77. 

Now  M=Mz±Ml=P2>±Ml=^  (72) 

But  " 


in  which  c  is  a  constant  depending  upon  the  condition  of  the  ends,  and 
the  manner  in  which  the  beam  is  loaded. 

Substituting  this  value  of  v  in  (72)  we  have 


COMPRESSION  AND  CROSS  BENDING  145 

and  reducing,  the  stress  due  to  cross  bending  is 

M,y, 
A=  --  pTi-  (73) 

*±-TE 

where  the  minus  sign  is  to  be  used  when  P  is  compression  and  the  plus 
sign  is  to  be  used  when  P  is  tension. 

The  factor  c  may  be  taken  equal  to  10  for  columns,  beams  and  bars 
with  hinged  ends  as  in  Fig.  77;  equal  to  24  where  one  end  is  hinged 
and  the  other  end  is  fixed  ;  and  equal  to  32  where  both  ends  are  fixed. 

The  total  stress  in  the  member  due  to  direct  stress  and  cross  bend- 
ing will  therefore  be  for  columns  with  hinged  ends 


(74) 


Formula  (74)  is  general,  and  applies  to  all  forms  of  sections  and 
all  forms  of  loading.  The  second  term  in  the  denominator  is  minus 
when  P  is  compression,  and  plus  when  P  is  tension. 

In  finding  the  stress  due  to  weight  of  member  and  direct  loading, 
the  value  for  f±  given  by  formula  (73)  must  be  multiplied  by  the  sine 
of  the  angle  that  the  member  makes  with  a  vertical  line. 

Combined  Compression  and  Cross  Bending.  —  The  method  of 
calculating  direct  and  cross  bending  stresses  will  be  illustrated  by  cal- 
culating the  stresses  in  the  end  post  of  a  bridge  due  to  direct  compres- 
sion, weight,  eccentricity  of  loading,  and  wind  moment. 

The  end  post  is  composed  of  two  io-Jnch  channels  weighing  15 
Ibs.  per  foot  with  a  14"  x  y±"  plate  riveted  on  the  upper  side  and  laced 
on  the  lower  side  with  single  lacing.  The  pins  are  placed 
in  the  center  of  the  channels  giving  an  eccentricity  of  e  =  1  .  44  inches. 
The  compressive  stress  P  produces  a  uniform  compression  on  all  fibres 
of  the  section  ;weight  of  the  member  causes  tension  on  the  lower  and  com- 
pression on  the  upper  fibres  ;  eccentricity  of  the  load  P  causes  compres- 
sion on  lower  and  tension  on  upper  fibres  ;  and  wind  moment  causes  com- 


146 


COMBINED  AND  ECCENTRIC  STRESSES 


U /  =  558  ins. «J 


Area  14  x*  PI-  =3-50  sq-in- 
Total  Area  =  12^42  »  " 

To  locate  neutral  axis  AA  take  momer  -5  about  lower  edge  of  channels 


Yo 


5-5X  10.125 


5.4  4- 


12.42 

.Eccentricity,  e  =  6.44-5.OO  =  1.44 


Moment  of  Inertia,  IA,  about  AA 
Let  IB  =1  of  H  about  axis  I-  1  =  133.8 
Ip/.=IofPJ-aboutaxis  2-2  =       .02 
As  =  Area  of  II  =  8-92  sq-in- 
Apl.=Area  of  PI-  =3-50  5q-  in- 
rhenIA=Ie  tABe2t!pi.  +APi.d2 


=  199.8 
Radius  of  gyration  ,  rA= 


4.0" 


Moment  of  Inertiaje,  about  B-B 
Let  Ig  =1  of  d  about  axis  5-3  =    4.6 
Ipi.  =1  of  R  about  axis  B-B  =  57-17 
As=Area  of  H  =  Q&Z  sq-in- 
Apl-Area  of  PI- =3-50  sq  in- 
ThenlB  =  lBtAB(4.25-H.64)2t  I  pi- 
=  4-6f  g-92(4.89)2+  57-17 
=  275-0 
Radius  of  gyration ,  rB = ^ff~§  -4.7 " 

' 


STRESS  DUE  To  WEIGHT  OF  MEMBER 

The  total  weight  of  the  member  is  as  follows:- 

2-IO"H  @I5*-30'-0'  long   •«   900.  Ibs. 
|-|4"X4"P|.@  1  1-9*30-0'     »         =357     >» 
Details  and  Lacing-26°/0  =    328     » 
Tota  I  wei'g  ht  ,  W,  =  I  5  8  5   " 

Bending  Moment  due  to  weight  of  the  member,  M  =gWlsin6 

Stress  due  to  weight,fw 


TOE 


- 


Stress  due  to  weight  in  upper  fibre 


fw= 


£  X  1585  X  358  X-633  X  3-81 

95300 


Ibs.  (compression) 


10X28000000 

Stress  due  to  weight  in  lower  fibre 

f'  =  |dix  MOO  =-1860  Ibs  (tension) 
3.0 1 


STRESS  DUE  TO  ECCENTRIC  LOADING 


STRESS  DUE  To  ECCENTRIC  LOADING 

The  stress  in  The  extreme  fibre  due  to  eccentric  loading  will  be 

f  _   MY<         Pey- 

re-^ELi==^E^ 

1    IOE         L     lOE. 
Eccentric  stress  in  upper  fibre 

,         95500X1.44X3.81 

fe  =  35500X355*    *  -  3347  lbs.(tension) 

l^9-6  "10X26  000  000 

Eccentric  stress  in  lower  fibre 

+  5657  lbs.(compre5Sion) 


The  resultant  stress  due  to  eccentric  loading  and  weight  will  be 

f.-fetfw 

=-3347  +  1100=^247  Ibsin  upper  fibre. 
=+5637-1860  =+3797  Ibs-  in  lower  fibre. 

The  maximum  stress  in  the  member  due  to  direct  loading,  weight 
Of  member  and  eccentric  loading  will  occur  in  the  lower  fibre  and 

willbe  f2+f,=g  +  fe  +  fw 

^\ 

=  ^f^P  +  3797  =  +  1/470  Ibs 

To  determine  the  position  of  the  pin  so  that  stress  due  to  weight 
will  neutralize  stress  due  to  eccentric   loading  make 

Pe'=§Wlsine  .where  e1  is  the  distance  of  the  pin 
oelow  The  neutral  axis. 

Substituting  and  solving  ,  95300xe'=  s(i3S5x358x.633) 

e'=.48H 


STRESS  DUE:  To  WIND  MOMENT 


H'=3^ooB 


R  =  6400 

n 


H=32ooi  ;_; 

V'=  12500  *V=IZ500 


2X 
ii  i 
TJ  i 


H'=3200 


R=6400 


Portal, Columns  Hinged. 
(a) 


Portal, Columns  Fixed.  Windward  Pedestal, 
(b)  (c) 


148  COMBINED  AND  ECCENTRIC  STRESSES 


Before  calculating  the  stress  due  To  wind  moment.it  will  be  necessary  to  de- 
termine whether  the  end  post  is  fixed  or  hinged- 

If  the  end  post  is  fixed.  the  negative  moment  developed  at  the  lower  pin 
will  be  M=t^=-520o_x*2§  =36/600  in  Ibs. 

In  order  to  obtain  this  condition  of  fixidity.the  stress  in  The  member  must 
develop  a  resisting  moment  equal  in  amount. 

Therefore  The  post  may  be  considered  fixed  if 

(95500  -V)  o  >   Hd 


or  -  Q  >  36|600 

but         347120  <  36I6OO   and  the  end  post  will  not  be  fixed. 
(While  This  is  The  usual  solution,  the  resisting  moment  certainly  reduces  The 
bending  moment  and  the  bending  stress  is  less  Than  computed  below-) 

The  maximum  moment  will  then  occur  at  the  foot  of  The  portal  knee 
brace  and  will  be   M  -3200x226-723200  in  Ibs- 

Stress  due  To  wind  moment  is  a  maximum  in  the   leeward  post  and  IS 
f        MV.  725200X7 

"l    -EL2  S.-,g     (95500  1  12500)353* 
lOt  10X28000000 

fw  =  ±£2480  Ibs. 

5tress,fw,is  compression  on  The  windward  side  and  tension  on  the  lee- 
ward side  of  the  member- 

pression  on  the  windward  and  tension  on  the  leeward  fibres.  The 
maximum  fibre  stress  will  come  at  the  foot  of  the  kne^.  brace  either  on 
the  upper  or  lower  fibres  on  the  windward  side  of  the  post,  depending 
upon  whether  the  stress  due  to  weight  is  greater  than  the  stress  due 
to  eccentric  loading,  or  the  reverse.  In  this  case  the  maximum  stress 
comes  on  the  lower  fibres  of  the  windward  side  of  the  post. 

Combined  Tension  and  Cross  Bending.  —  The  stress  due  to 
cross  bending  when  the  member  is  also  subjected  to  direct  tension  is 
given  by  the  formula 


the  nomenclature  being  the  same  as  in  (74).    The  constant  c  is  taker- 
equal  to  10  where  the  ends  are  hinged. 


STRESS  IN  BARS  DUE  TO  WEIGHT  H9 

Stress  in  a  Bar  Due  to  its  Own  Weight:  — 

Let  b  =  breadth  of  bar  in  inches  ; 
h  =:  depth  of  bar  in  inches  ; 

•w  =  weight  of  bar  per  lineal  inch  =  0.28  b  hf; 

p 

f2  =         ,  =  direct  unit  stress. 
b  h 

We  will  also  have 
3'i  =  l/*   h'> 

M,  =  ys  w  I2-, 

P  =  f,  b  h. 

Substituting  in  (75)  we  have 


. 

~~      b  h\   i 

TT    "  10  X  28.000,000 

4.900,000  h 


/2  +23,000, 000  (j 

where  /t  is  the  extreme  fibre  stress  in  the  bar  due  to  weight,  and  is 
tension  in  lower  fibre  and  compression  in  upper  fibre. 

If  the  bar  is  inclined,  the  stress  obtained  by  formula  (76)  must  be 
multiplied  by  the  sine  of  the  angle  that  the  bar  makes  with  a  vertical 
line. 

Formula  (76)  is  much  more  convenient  for  actual  use  than  for- 
mula (75). 

Diagram  for  Stress  in  Bars  Due  to  Their  Own  Weight. — Tak- 
ing the  reciprocal  of  (76)  we  have 

23,000,000  (A)2 
7i^  4,900,000  h   ~ 


and  fl  -.  ' 


5o 


COMBINED  AND  ECCENTRIC  STRESSES 


Fig.  78  gives  values  of  y^  for  different  values  of  f2,  and  values 
of  y2  for  different  values  of  the  length  in  feet,  L.  The  values  of  y^ 
and  y2  can  be  read  off  the  diagram  directly  for  any  value  of  h,  /2,  and 
L.  And  then,  if  the  sum  of  y^  and  yz  be  taken  on  the  lower  part  of  the 


05 


I  1.5         2  3          4       5      6     7    6  9  10 

I&II. Depth  of  Bar  in  Inches 
lll.Yt+rz  in  Tens  of  Thousandths 


15        20 


FIG.  78.    DIAGRAM  FOR  FINDING  STRESS  IN  BARS  DUE  TO  THEIR  OWN 

WEIGHT. 


DIAGRAM  FOR  FINDING  STRESS  IN  BARS  151 

diagram,  the  reciprocal,  which  is  the  fibre  stress  flt  may  be  read  off  the 
right  hand  side. 

The  use  of  the  diagram  will  be  illustrated  by  two  problems : 
Problem  I.    Required  the  stress  in  a  4"  x  i"  eye-bar,  20  feet  long, 
which  has  a  direct  tension  of  56,000  Ibs. 

In  this  case,  h  —  4",  L  =  20  ft.,  and  f2  =  14,000  Ibs.  per  sq.  in. 
The  stress  due  to  weight,  flf  is  found  as  follows:  On  the  bottom  of 
the  diagram  find  h  =  4  inches,  follow  up  the  vertical  line  to  its  inter- 
section with  inclined  line  marked  L  =  20,  and  then  follow  the  horizontal 
line  passing  through  the  point  of  intersection  out  to  the  left  margin  and 
find  TO  =  3.3  tens  of  thousandths ;  then  follow  the  vertical  line  h  =  4 
inches,  up  to  its  intersection  with  inclined  line  marked  f2  =  14,000,  and 
then  follow  the  horizontal  line  passing  through  the  point  of  intersection 
out  to  the  left  margin  and  find  jx  =  7.2  tens  of  thousandths. 

Now  to  find  the  reciprocal  of  y^  +  v,  =  7.2  +  3.3  =  10.5,  find  value 
of  y±  +  yz  =  10.5  on  lower  edge  of  diagram,  follow  vertical  line  to  its 
intersection  with  inclined  line  marked  "Line  of  Reciprocals"  and  find 
stress  /x  by  following  horizontal  line  to  right  hand  margin  to  be 

/±  =  950  Ibs.  per  sq.  in. 

By  substituting  in  (76)  and  solving  we  get  /^  =  960  Ibs.  per  sq.  in. 

Problem  2.  Required  the  stress  in  a  5"  x  J^"  eye-bar,  30  feet  long, 
which  has  a  direct  tension  of  60,000  Ibs.,  and  is  inclined  so  that  it  makes 
an  angle  of  45°  with  a  vertical  line. 

In  this  case,  h  =  5",  L  =  30  feet,  f2  =  16,000  Ibs.,  and  0  =45°. 
From  the  diagram  as  in  Problem  i,  yz  =  1.8  fens  of  thousandths,  and 
Y!  =  6.5  tens  of  thousandths,  and 

/i  =  y   +y    sin  e  =  120°  X  sin  6 
=  850  Ibs.  per  sq.  in. 

Relations  between  h,  flt  fz  and  L.  For  any  values  of  f2  and  L,  fl 
will  be  a  maximum  for  that  value  of  h  which  will  make  3^  +  yz  a  min- 


152  COMBINED  AND  ECCENTRIC  STRESSES 

imum.  This  value  of  h  will  now  be  determined.  Differentiating  equa- 
tion (76)  with  reference  to  /x  and  h,  we  have  after  solving  for  h 
after  placing  the  first  derivation  equal  to  zero 

6  =       ''  (78) 


in  which  h  is  the  depth  of  bar  which  will  have  a  maximum  fibre 
stress  for  any  given  values  of  /  and  f2. 

Now  if  we  substitute  the  value  of  h  in  (78)  back  in  equation  (76), 
we  find  that  f1  will  be  a  maximum  when  y1  =  y2. 

Now  in  the  diagram  the  values  of  y^  and  y2  for  any  given  values 
of  /g  and  L  will  be  equal  for  the  depth  of  bar,  h,  corresponding  to  the 
intersection  of  the  /2  and  L  lines. 

It  is  therefore  seen  that  every  intersection  of  the  inclined  /2  and  L, 
lines  in  the  diagram,  has  for  an  abscissa  a  value  of  h,  which  will  have  a 
maximum  fibre  stress  f1}  for  the  given  values  of  /2  and  L. 

For  example,  for  L  =  30  feet  and  /2  =  12,000  Ibs.  we  find  h  = 
8.3  inches  and  /±  =  1700  Ibs.  For  the  given  length  L  and  direct  fibre 
stress  f2,  a  bar  deeper  or  shallower  than  8.3  inches  will  give  a  smaller 
value  of  /j  than  1700  Ibs. 

Eccentric  Riveted  Connections.  —  The  actual  shearing  stresses 
in  riveted  connections  are  often  very  much  in  excess  of  the 
direct  shearing  stresses.  This  will  be  illustrated  by  the  calculation 
of  the  shearing  stresses  in  the  rivets  in  the  standard  connection  shown 
in  Fig.  79  and  Fig.  80. 

The  eccentric  force,  P,  may  be  replaced  by  a  direct  force,  P,  acting 
through  the  center  of  gravity  of  the  rivets  and  parallel  to  its  original 
direction,  and  a  couple  with  a  moment  M  =  P  x  3"  =  60,000  inch-lbs. 
Each  rivet  in  the  connection  will  then  take  a  direct  shear  equal  to  P 
divided  by  n,  where  n  is  the  total  number  of  rivets  in  the  connection, 
and  a  shear  due  to  bending  moment  M. 

The  shear  in  any  rivet  due  to  moment  will  vary  as  the  distance, 


ECCENTRIC  RIVETED  CONNECTIONS 


'53 


and  the  resisting  moment  exerted  by  each  rivet  will  vary  as  the  square 
of  the  distance  of  the  rivet  from  the  center  of  gravity  of  all  the  rivets. 
Now,  if  a  is  taken  as  the  resultant  shear  due  to  bending  moment  in 
a  rivet  at  a  unit's  distance  from  the  center  of  gravity,  we  will  have  the 
relation 

M  =  a  (d,2  +  d*  +  d*  +  dS  +  </62) 


and 


M 


a   = 


(79) 


The  remainder  of  the  calculations  are  shown  in  Fig.  79.    The  re- 
sultant shears  on  the  rivets  are  given  in  the  last  column  of  the  table 


Direct  Shear  S  =  20000  4-  5  =  4000  Ibs- 
Moment  =  20OOO  x  3  =  600OO  in  Ibs- 


Where  a 


Moment  shear  on  rivet  3 
Ibs- 


Rivet 

d 

d* 

Moment 

M 

S 

R 

1 
I 
3 
4 
5 

^.70 
1.90 
1.00 
1  90 
£.70 

7.29 

3-61 
1-00 
3.61 
729 

19/85 
9500 

a&50 

9500 
19185 

7100 
5000 
£630 
5000 
7100 

4000 
4000 
4000 
4000 
4000 

9300 
3?00 
6630 
3200 
9300 

a  Zd2=  ^^SOa=60000  in  Ibs. 

20000 

a  =  2630  1  bs-  =  moment  shear  on  rivet  3 

M  =  Shear  due  to  Moment . 

S  =  Shear  due  to  Direct  Load ,  P 

R  -  Resultant  Shear  - 

O          4000      8000      I200O 


FIG.  79. 


and  are  much  larger  than  would  be  expected. 

The  force  and  equilibrium  polygons  for  the  resultant  shears  and 
load  P,  drawn  in  Fig.  80,  close,  which  shows  that  the  connection  is  in 

equilibrium. 


COMBINED  AND  ECCENTRIC  STRESSES 


Equilibrium  Polygon 


0  4OOO       8OOO      IZOOO 


Standard  Connection 


*  Force  Polygon 


FIG.  80. 

STRESSES  IN  PINS. — A  pin  under  ordinary  conditions  is  a 
short  beam  and  must  be  designed  (i)  for  bending,  (2)  for  shear,  and 
(3)  for  bearing.  If  a  pin  becomes  bent  the  distribution  of  the  loads 
and  the  calculation  of  the  stresses  are  very  uncertain. 

The  cross  bending  stress,  S,  is  found  by  means  of  the  fundamental 

Me 
formula  for  flexure,  S  = ,  where  the  maximum  bending  moment 

M,  is  found  as  explained  later;  /  is  the  moment  of  inertia,  and  c  is  the 
radius  of  a  solid  or  hollow  pin. 

The  safe  shearing  stresses  given  in  standard  specifications  are 
for  a  uniform  distribution  of  the  shear  over  the  entire  cross  section, 
and  the  actual  unit  shearing  stress  to  be  used  in  designing  will  be  equal 
to  the  maximum  shear  divided  by  the  area  of  the  cross  section  of  the  pin. 

The  bearing  stress  is  found  by  dividing  the  stress  in  the  member 
by  the  bearing  area  of  the  pin,  found  by  multiplying  the  thickness  of 
the  bearing  plates  by  the  diameter  of  the  pin. 


STRESSES  IN  PINS. 


155 


Force  D<agram--5tre55e5  U|. 

- }/ 208600  *  +2d5300 ' 

FIG.  Sob.    CALCULATION  OF  STRESSES  IN  A  PIN  BY  ALGEBRAIC  MOMENTS. 

Calculation  of  Stresses. — The  method  of  calculation  will  be  il- 
lustrated by  calculating  the  stresses  in  the  pin  at  t/x  in  (a)  Fig.  Sob. 
In  the  complete  investigation  of  the  pin  Ult  it  would  be  necessary 
to  calculate  the  stresses  when  the  stress  in  U±  U2  was  a  maximum,  and 
when  the  stress  in  U±  L2  was  a  maximum.  Only  the  case  where  the 
stress  in  U^  U2  is  a  maximum  will  be  considered.  However,  maximum 
stresses  in  pins  sometimes  occur  when  the  stress  in  Ut  L2  is  a  maximum, 
and  this  case  should  be  considered  in  practice. 

Bending  Moment. — The  stresses  in  the  members  are  shown  in 
(c),  which  gives  the  force  polygon  for  the  forces.  The  makeup  of  the 
members  is  shown  in  (a),  and  the  pin  packing  on  one  side  is  shown  in 
(b).  The  stresses  shown  in  (c)  are  applied  one-half  on  each  side  of  the 
member,  the  pin  acting  like  a  simple  beam.  The  stresses  are  assumed 
as  applied  at  the  centers  of  the  members. 

Algebraic  Method. — The  amounts  of  the  forces  and  the  distances 
between  their  points  of  application  as  calculated  from  (b)  are  shosvn 
in  (d).  The  horizontal  and  vertical  components  of  the  forces  are 
considered  separately,  the  maximum  horizontal  bending  moment  and 

12 


156  COMBINED  AND  ECCENTRIC  STRESSES. 

the  maximum  vertical  bending  moment  are  calculated  for  the  same 
point,  and  the  resultant  moment  is  then  found  by  means  of  the  force 
triangle. 

In  (d)  the  horizontal  bending  moments  are  calculated  about  the 
points  i,  2,  3,  4;  the  maximum  horizontal  moment  is  to  the  right  of  3, 
and  is  208,600  Ib.-in.  The  vertical  bending  moments  are  calculated 
about  points  5,  6,  7,  8 ;  the  maximum  vertical  bending  moment  is  to 
the  right  of  8,  and  is  283,000  Ib.-in.  The  maximum  bending  moment  is 
at  and  to  the  right  of  4  and  8,  and  is  V2o8,6oo2  +  283,ooo2  =  351,600 
Ib.-in. 

Me 

Substituting  in  the  formula  S  = ,  the  maximum  bending  stress 

is  S  =  16,600  Ibs.  The  allowable  bending  stress  for  which  this  bridge 
was  designed  was  18,000  Ibs. 

Graphic  Method. — The  amounts  of  the  forces  and  the  distances 
between  their  points  of  application  are  shown  in  (b)  Fig.  8oc.  The  force 
polygon  for  the  horizontal  components  is  given  in  (c),  and  the  bending 
moment  polygon  is  given  in  (a).  The  maximum  horizontal  bending 
moment  is  to  the  right  of  3,  and  is  H  X  3^  =  200,000  X  1.04  =  208,000 
Ib.-in.  The  force  polygon  for  the  vertical  forces  is  given  in  (d)  and 
the  bending  moment  polygon  is  given  in  (e).  The  maximum  vertical 
bending  moment  is  to  the  right  of  8,  and  is  H  X  y  =  200,000  X  142 
=  284,000  Ib.-in.  The  maximum  bending  moment  occurs  at  and  to  the 
right  of  4  and  8,  and  is  351,000  Ib.-in.,  as  shown  in  (f). 

Shear. — The  shear  is  found  for  both  the  horizontal  and  vertical 
components  as  in  a  simple  beam,  and  is  equal  to  the  summation  of  all 
the  forces  to  the  left  of  the  section.  The  horizontal  shear  diagram  is 
shown  in  (g),  and  the  vertical  shear  diagram  is  shown  in  (h).  The 
maximum  horizontal  shear  is  between  I  and  2,  and  is  165,400  Ibs.  The 
shear  between  2  and  3  is  165,400  —  99,300  =  66,100  Ibs.  The  maxi- 
mum vertical  shear  is  between  6  and  7,  and  is  126,300  Ibs.  The  result- 
ant shear  between  2  and  3  and  6  and  7  is  V  i26,3OO2-{-66,ioo2=i45,ooo 
Ibs.  as  in  (i),  which  is  less  than  the  horizontal  shear  between  i  and  2. 
The  maximum  shear  therefore  comes  between  i  and  2,  and  is  165,400 
Ibs.  The  maximum  shearing  unit  stress  is  5750  Ibs.  The  allowable 
shearing  stress  was  9000  Ibs. 

Bearing. — The  bearing  stress  in  L0  C7±  is  165,650-^6X1.94  = 
14,300  Ibs.  Bearing  stress  in  U±  U2  is  165,400-7-6X1.88=14,600 


STRESSES  IN  PINS. 


157 


Horizontal  Moment  Polygon, 
(a)         b 

o      " 


Force  Polygon, 
Horizontal  Comp. 


Horizontal vShear  Diagram.      » 
/-l  7'! 

(h)  -- 


flnnrnt' 


Vertical^hear  Diagram. 

Maximum  Shear =16 5400* 


"-<     rorce 

-y  Vertical  Comp. 
Design  of  Pin. 

E>end!noj  Moment 

--551600*" 

Allowable  Rending  Moment 
for  0  pin,  using  fiber  stress 
;  18000* (page  Wt  Cambria) 

'301700*" 

f1a*in->um  Shear  •  165400 
Ac ft/a/  Fibfr  Stress  --  5750  * 
Al/owai>!e 


FIG.  8oc.    CALCULATION  OF  STRESSES  IN  A  PIN  BY  GRAPHIC  MOMENTS. 


Ibs.  Bearing  stress  in  U^  L^  is  42,200-^-6X0.89^7900  Ibs.  Bear- 
ing stress  in  Ui  L2  is  107,000-^- 6  X  1^=12,400  Ibs.  The  allowable 
bearing  stress  was  15,000  Ibs. 


CHAPTER  XVa. 
GRAPHIC  METHODS  FOR  CALCULATING  THE  DEFLECTION  OF  BEAMS. 

Introduction. — Algebraic  methods  for  calculating-  the  deflection 
of  beams  and  the  reactions  of  continuous  beams  are  given  in  detail 
in  standard  works  on  applied  mechanics.  The  graphic  methods  are, 
however,  not  given  the  attention  that  their  elegance  and  simplicity 
merit.  The  underlying  principles  of  the  graphic  method  will  be  de- 
veloped and  a  few  applications  of  the  method  will  be  given  in  the 


re) 


FIG.  i. 


following  discussion.     The  discussion  will  be  limited  to  beams  with 
a  constant  moment  of  inertia. 

Graphic  Equation  of  the  Elastic  Curve. — Load  a  simple  beam 
with  a  continuous  load  represented  by  the  equation  y  =  fx,  as  in  (a) 


EQUATION  OF  ELASTIC  CURVE  J59 

Fig.  i.  Assume  that  each  differential  load,  y  dx  =  fx  dx,  acts  through 
its  center  of  gravity.  Now  construct  a  force  polygon  as  in  (c)  and 
an  equilibrium  polygon  as  in  (b)  Fig.  I. 

Now,  in   (b)   the  tangent  of  the  angle  between  any  side  of  the 

dy 

equilibrium  polygon  and  the  X-axis  is  tan  a  =  —  .     If  the  string  b  o  in 

d  x 

(b)  is  produced  until  it  cuts  the  vertical  line  through  3,  it  will  cut  off 
the  intercept  3-31,  which  is  the  difference  between  two  consecutive 
values  of  d  y  and  therefore  equals  d2  y, 

Now,  it  has  been  proved  that  the  moment  of  the  force  acting 
through  point  2  in  (b)  about  point  3,  is  equal  to  the  intercept  3-31 
multiplied  by  the  pole  distance  H,  is  equal  to  3-31  X  H  =  d2  y  H. 
But  the  moment  of  the  differential  load  fx  dx,  which  acts  through 
point  2,  about  point  3,  is  fx  dx2,  and 


fx  dx2  =  d-y  H 
and 


<•> 


It  is  evident  that  (i)  is  the  differential  equation  of  the  equi- 
librium polygon  in  (b). 

Now,  if  the  loading  is  taken  so  that  y  =  fx  =  M,  where  M 
represents  the  bending  moment  at  any  given  point  x,  due  to  a  given 
loading,  the  equation  for  the  equilibrium  polygon  becomes 

d*v       M 


From  mechanics  we  have  the  relation  that 

^  =  -  (3) 

AH      El 

which  differs  from  (2)  only  in  having  El  substituted  for  H,  E  being 

the  modulus  of  elasticity  and  /  the  moment  of  inertia  of  the  given  beam. 

This   relation  may  be   deduced   as   follows:   In    (d)    Fig.    j,   let 

equilibrium  polygon  1-2-3  represent  the  neutral  axis  of  a  beam  as  in 


160  DEFLECTION  OF  BEAMS 

(a),  the  points  I,  2  and  3  being  at  a  distance  dx  apart.  The  distortion 
will  be  assumed  to  be  so  small  that  d  I  =  dx.  Now,  the  triangle  2-O-3 
may  be  taken  as  similar  to  triangle  3-2.-31  for  small  distortions,  and 

O-2  12-3::  2-3  :  3-31 
but  0-2  equals  Rf  2-3  equals  dx,  and  3-31  equals  d-y,  and,  therefore, 


Now,  in  a  beam  as  in  (e)  Fig.  I,  the  stresses  at  any  point  in  the 
beam  will  vary  as  the  distance  from  the  neutral  axis,  and  from  similar 
triangles  we  have 

R  :  dx  ::  c  :  A 
and 

R±  =  cdx  (5) 

Now,  if  5  is  the  fiber  stress  on  the  extreme  fiber,  and  E  is  the 
modulus  of  elasticity,  we  have 

A  :  5  :  :  d.v  :  E 

*E  =  Sd.v  (6) 

and,  solving  (5)  and  (6)  for  R,  we  have 


But  from  the  common  theory  of  flexure  we  have  M  c  =  SI,  and 
substituting 

El 


Substituting  the  value  of  R  in  (7)  and  (4)  we  have 


The  preceding  discussion  gives  the  following  simple  graphic  method 
for  constructing  the  elastic  curve  of  a  beam  : 

Construct  the  bending  moment  polygon  for  the  given  loading  on 
the  beam.  Load  the  beam  with  this  bending  moment  polygon,  and 


SIMPLE  BEAM  161 

with  a  force  polygon  having  a  pole  distance  equal  to  E  l>  construct 
an  equilibrium  polygon;  this  polygon  will  be  the  elastic  curve  of  the 
beam.  It  is  not  commonly  convenient  to  use  a  pole  distance  equal  to 
E  I,  and  a  pole  distance  H  is  used,  where  N  H  equals  E  I ;  the  de- 
flection at  any  point  will  then  be  equal  to  the  measured  ordinate  di- 
vided by  N. 

Simple  Beam. — The  simple  beam  will  be  considered  when  loaded 
with  concentrated  and  uniform  loads,  using  both  algebraic  and  graphic 
methods. 

Algebraic  Method — Concentrated  Load  at  Center  of  Beam. — The 
simple  beam  in  (a)  Fig.  2,  is  loaded  with  a  load  P  at  the  center.  The 
bending  moment  diagram  is  shown  in  (b)  and  the  beam  is  loaded  with 
the  bending  moment  diagram  in  (c)  Fig.  2. 

To  find  the  equation  of  the  elastic  curve  take  moments  of  the 
forces  to  the  left  of  a  point  at  a  distance  -x  from  the  left  support,  and 

PL2.r       Px* 

—  EIy=-— 

16  12 

and 

.-    .      .  .         xxr  ^ 

(Cf) 


fo/  PL*  ot  PL  *f  fo'.n/Z.J 

K'*76~R*W  **& 

(C) 

FIG.  2.  FIG.  3. 

The  maximum  deflection  will  occur  when  x  =  y2L  in  (8),  or  it 
may  be  found  by  taking  moments  of  forces  to  left  of  x  =  l/2  L  to  be 

PL3 

Co) 


48E7 
Beam   Uniformly  Loaded.  —  The  simple  beam  in    (a)    Fig.   3,  is 


1 62 


DEFLECTION  OF  BEAMS 


loaded  with  a  uniform  load  of  w  per  lineal  foot.  The  bending  mo- 
ment parabola  is  shown  in  (b),  and  the  beam  is  loaded  with  the 
bending  moment  parabola  in  (c)  Fig.  3.  To  find  the  equation  of  the 
elastic  curve,  take  moments  of  forces  to  the  left  of  a  point  at  a  dis- 
tance x  from  the  left  support. 

The  equation  of  the  bending  moment  parabola  with  the  origin 
of  co-ordinates  at  the  left  support  is  y  =  ^2  w  L  x  —  l/2iv  x2,  the  area 
of  a  segment  of  the  parabola  is  A  =  %w  L  x2  —  1-6  w  xz,  and  the 
center  of  gravity  measured  back  from  x  is 

X(2L—  X) 


6L  —  4X 

Taking  moments  of  forces  to  the  left  of  a  point  x,  and  reducing, 
we  have 

The  deflection  is  a  maximum  when  x  =  y2  L,  and  may  be  found 
directly  by  taking  moments,  or  may  be  found  from  (10),  and  is 


384  EI 

Cantilever  Beam — Concentrated  Load. — The  cantilever  beam  in 
(a)  Fig.  4,  has  a  concentrated  load,  P ,  at  its  extreme  end.  It  will 
be  seen  that  the  cantilever  beam  may  be  considered  as  one-half  of  a 
simple  beam  with  a  span  2  L,  and  a  load  2P,  at  the  center.  The 
equation  of  the  elastic  curve  may  be  found  as  in  Fig.  2.  Load  the 
beam  with  the  bending  moment  diagram  as  in  (b)  Fig.  4,  and  consider- 
ing the  cantilever  as  one-half  of  the  simple  beam  we  have,  after  re- 
ducing, 

6EIy  =  3PL2.v  —  P.v*  (12) 


*>!«—*  ---- 

PL*  H  -  x  -  *^&"t 


<t>) 

FIG.  4. 


i 

--aci 


SIMPLE  BEAM  163 

The  maximum  value  of  A  is  equal  to  y  when  x  equals  Lf  and 

PL3 


A=^7  (I3) 

To  find  the  maximum  deflection  we  may  take  the  moment  of  the 
entire  bending-moment  parabola  about  the  point  I,  and 

PL2         2 

== X~£,and 

2  3 

PL3 


This  method  of  finding  the  maximum  deflection  of  a  cantilever 
beam  is  the  one  to  use  in  calculations,  and  will  be  used  in  the  solu- 
tion of  the  problem  of  the  transverse  bent. 

Simple  Beam — Graphic  Method. — In  Fig.  5  a  simple  beam  is 
loaded  with  a  load  P,  as  shown.  With  force  polygon  (b),  draw 
equilibrium  polygon  (c).  Now  load  the  beam  with  equilibrium  polygon 
as  in  (c),  and  divide  the  area  of  the  equilibrium  polygon  into  segments, 
which  are  treated  as  loads  acting  through  their  centers  of  gravity.  Con- 
struct force  polygon  (d)  and  draw  equilibrium  polygon  (e). 

Now,  the  deflection  at  any  point  having  an  ordinate  y  in  (e)  will 
be,  if  proper  scales  are  used, 

_yXHXHl 
El 

In  Fig.  5,  if  P  equals  3000  Ibs.,  and  the  area  of  the  equilibrium 
polygon  and  pole  distance  H1  are  measured  in  square-foot  pounds, 
pole  distance  H  in  pounds,  and  y  in  feet,  we  will  have 

v  V  H  V  H1  V  1728 

y    S\    "     XN    •*•*        /\     JL/^O 


=  1.88    inches    at    center,    while    maximum    value    of    deflection    is 
A1  =  1.92  inches. 

Tangents  to  Elastic  Curve. — If  strings   I   and  3  in   (e)   be  pro- 


i64 


DEFLECTION  OF  BEAMS 


duced,  they  will  intersect  at  2  on  a  line  through  the  center  of  gravity 
of  the  moment-area  polygon,  and  the  strings  1-2  and  2-3  will  be 
tangents  to  the  elastic  curve  at  the  supports  7^  and  R2,  respectively. 
This  gives  an  easy  method  of  constructing  the  tangents  to  the  elastic 
curve  without  constructing  the  curve.  It  is  also  seen  that  the  tan- 


....  /6 


10 


g£ L^.l^o1 

o*   -  - — U   »>^i 


gents  to  the  elastic  curve  depend  only  on  the  amount  of  the  moment 
area  and  position  of  its  center  of  gravity,  and  are  independent  of  the 
arrangement  of  the  moment  areas. 

Continuous  Beams. — A  beam  which  in  an  unstrained  condition 
rests  on  more  than  two  supports  is  a  continuous  beam.  For  a  straight 
beam  the  supports  must  all  be  on  the  same  level.  Beams  of  one  span 
with  one  end  fixed  and  the  other  end  supported,  or  with  both  ends 
fixed,  may  also  be  considered  as  continuous  beams. 

In  Fig.  6a  the  continuous  beam  in  (a)  with  spans  Lj  and  L2  carries 
a  uniform  load  w  per  lineal  foot.  It  is  required  to  calculate  the  re- 
actions Rlf  R2,  and  R3. 


CONTINUOUS  BEAM  165 

The  reactions  of  the  continuous  beam  in  (a)  may  be  replaced  by 
the  reactions  of  the  two  simple  beams  loaded  with  the  uniform  load  w 
in  (b),  and  the  reactions  and  the  load  of  the  simple  beam  with  the  span 
Lj  -\-  L2  and  carrying  a  negative  load  r2'  in  (c).  The  reactions  in  (a) 
will  then  have  the  following  values  ;  Ri  =  r1  —  r/  ;  R2  =  r2  -\-  r2r  ; 
Rs  =  r3  —  rz'. 

Now  the  upward  curvature  of  the  beam  in  (a)  due  to  the  load  r2r 
will  be  neutralized  by  the  load  above  equal  to  r2  which  is  transferred 
to  the  reaction  R2  by  flexure  in  the  beam.  The  upward  deflection  of 


w  per  //>?.  ft. 

x&/////////y/^^ 


<«> 


ww//ft-ttytffflM 

t 


the  beam  in  (c)  at  any  point  will  be  the  bending  moment  divided  by  E  I 
at  the  same  point  in  (d)  due  to  a  bending  moment  polygon  with  a  maxi- 
mum moment  M2  =  r/  X  L±  =  rB'  X  £2  \  and  the  downward  deflection 
of  the  beam  in  (b)  at  any  point  will  be  the  bending  moment  divided 
by  E  I  at  the  same  point  in  (d)  due  to  the  bending  moment  polygons 
for  a  uniform  load  w  covering  the  simple  spans  in  (b).  But  the  de- 
flection of  the  beam  in  (a)  is  zero  at  the  reaction  R2,  and  therefore  the 
bending  moment  at  the  corresponding  point  in  (d)  is  zero. 


1  66  DEFLECTION  OF  BEAMS 

From  the  above  discussion  it  follows  that  to  calculate  the  reactions 
of  the  continuous  beam  in  (a)  by  moment  areas,  take  a  simple  beam 
with  a  span  equal  to  L±  +  L2,  and  load  it  with  the  bending  moment 
polygons  for  beams  (b)  and  (c)  as  in  (d)  ;  the  bending  moment  in 
beam  (d)  at  the  points  corresponding  to  the  reactions  will  be  equal  to 
zero,  and  the  reactions  of  beam  (a)  can  be  calculated  by  statics  when 
the  M2  is  obtained. 

Continuous  Beam  —  Concentrated  Loads.  —  In  (a)  Fig.  6,  a  con- 
tinuous beam  of  two  equal  spans  of  length  L,  is  loaded  with  two 
equal  loads  P,  at  the  centers  of  the  spans.  Calculate  the  bending 


FIG.  6. 

moments  and  load  a  simple  beam  with  a  span  equal  to  2  L,  with  the 
bending-moment  diagrams  due  to  P  in  each  span,  and  with  the  nega- 
tive bending-moment  diagram  due  to  the  reaction  R2.  Then  to  find 
M2,  the  bending  moment  at  2,  take  moments  of  forces  to  the  left  of 
2,  and 

M2L2       PL*       M2L2       PL3 

6 


=  —  —  PL 
16 


To  calculate  R1  take  moments  in  (a)  about  2,  and 

PL 

R^L M2  ==  o 

2 


CONTINUOUS  BEAM 


and 

'-•  ;'"*-  T' 

-B^zm  Uniformly  Loaded.  —  In  (a)  Fig.  7,  a  continuous  beam 
of  three  equal  spans  of  length  L,  is  loaded  with  a  uniform  load  equal 
to  w  per  foot.  Calculate  the  bending  moments  due  to  a  uniform  load 
of  w  on  each  span,  and  load  a  simple  beam  of  span  3  L  with  the  posi- 
tive bending-moment  diagrams  due  to  load  ziv,  and  with  the  negative 
bending-moment  diagrams  due  to  the  reactions  R2  and  Rs.  The 
bending  moment  M2  is  equal  to  Ms.  Now  the  deflection  of  the  beam 
is  zero  at  2  and  3,  and  the  bending  moments  must,  therefore,  be  zero 
at  these  points.  Taking  moments  of  forces  to  the  left  of  2,  we  have 


I       k 

C"vj/Z*J      */%    fWf    <-/^»    I  w£*     y 

\    6  8  8     / 

\  /  9  f 


FIG.  7. 

wL4        K-L*       Jl/2L2 
"^~       ~2T         ~^" 

10 

To  calculate  Rl  take  moments  about  2  in  (a),  and 

*'  L2 

2 

4 
10 


i68 


DEFLECTION  OF  BEAMS 


A_ 
10 


II 

10 


Continuous  Beam  of  n  Spans. — To  calculate  the  reactions  for  a 
continuous  beam  of  n  spans,  equal  or  unequal,  loaded  with  any  system 
or  systems  of  loads  proceed  as  follows : 

Calculate  the  bending  moment  due  to  the  external  load,  or  loads, 
or  system  of  loads  in  each  span  considered  as  a  simple  beam.  Take 
a  simple  beam  having  a  total  length  equal  to  the  length  of  the  con- 
tinuous beam,  and  load  it  with  the  bending  moment  polygons  found 
as  above.  Also  load  the  beam  with  the  bending  moment  polygons  due 
to  the  reactions.  The  reactions  being  unknown,  the  bending  moments 
at  the  reactions  will  be  unknown.  Now  calculate  the  bending  moment 
in  the  simple  beam  at  points  corresponding  to  each  reaction  and  place 
the  result  equal  to  zero,  for  the  reason  that  the  deflection  at  the  sup- 
ports is  zero. 

For  a  continuous  beam  of  n  spans  there  will  be  n  +  I  equations 
which  is  equal  to  the  number  of  unknown  reactions.  Solving  these 
equations  the  unknown  moments  will  be  found,  and  the  reactions  may 
be  calculated  algebraically. 

Transverse  Bent. — The  problem  of  the  calculation  of  the  point 
of  contra-flexure  in  the  columns  of  a  transverse  bent — the  algebraic 


FIG.  8. 


solution  of  which  is  given  in  Chapter  XI  —  will  now  be  solved  by  the 
use  of  moment  areas.     The  nomenclature  in  Fig.  8  is  the  same  as  in 


REACTIONS  OF  DRAW  BRIDGES  169 

Chapter  XL     It  is  assumed  that  the  deflection  at  points  b  and  c  are 
equal. 

In  (b)  Fig.  8,  the  deflection  at  b  from  the  tangent  at  a  is  found 
by  taking  moments  of  the  moment  areas  below  b  to  be 


6EI 


(14) 


The  deflection  at  c   from  the  tangent  at  a  is  found  by  taking 
moments  of  moment  areas  below  c  to  be 

Md  2M1(h  —  d)2         M,d 

-(*  —  2/3d) 


6E  I 


But  A  is  equal  to  A1  by  hypothesis,  and  equating  (14)  and  (15) 
we  have 

2M0d2  —  Mid2  =  M0  ($dh  —  d2)—  Mx  (2h2  —  hd) 

transposing, 

M0  (zhd  —  z  d2)  =  M,  (2  h*  —  hd  —  d2)  (16) 

Now  in  (c)  Fig.  8,  it  will  be  seen  that  M0  :  Mt  ::  y0  :  d  —  y0, 
and 

Jf.(rf  —  y0)=3f1y.  (17) 

Solving  (16)  and  (17)  for  y0,  we  have 

d     (2h  +  d) 

y0  =  -  ,.  ,     .,  (18) 

2    (/I  +2  rf  ) 

which  is  the  same  value  as  was  found  by  algebraic  methods. 

Reactions  of  Simple  Draw  Bridges.  —  The  preceding  methods  are 
not  adapted  to  the  solution  of  problems  involving  moving  loads,  as 
in  draw  bridges.  The  following  method,  which  is  an  application  of 
curved  influence  lines,  is  quite  simple  in  theory  and  application,  al- 


7o 


DEFLECTION  OF  BEAMS 


though  requiring  considerable  labor  in  preparing  the  diagrams.     The 
solution  will  first  be  explained  and  a  proof  given  later : 

Draw  Bridge  With  Three  Supports. — In  Fig.  9  a  continuous 
beam  with  spans  L±  and  L2  is  loaded  with  concentrated  moving  loads 
represented  by  P±  and  P2,  as  in  (a). 


k---£T--> 
I                        > 

k—  --  b 
'/         Zl 

—  >J 

1 

^J 

^f__t^ 

-1 

1 

J 

re) 

FIG.  9. 

"^1 

^ 


In  (b)  load  a  simple  beam  having  a  span  Lj  -f-  L2  with  a  bend- 
ing-moment  polygon  due  to  the  reaction  R2  (the  value  of  R2  is  unknown, 
and  any  convenient  load  will  do). 

Divide  the  bending-moment  diagram  into  segments,  construct  a 
force  polygon  as  in  (d)  and  draw  an  equilibrium  polygon  as  in  (c) 


REACTIONS  OF  DRAW  BRIDGES.  171 

Fig.  9,  assuming  that  the  segments  are  loads  acting  through  their  cen- 
ters of  gravity. 

The  pole  distance  H  may  be  taken  as  any  convenient  length,  and 
the  pole  O  may  be  taken  at  any  point  [in  (c)  the  pole  has  been  selected 
to  bring  the  closing  line  horizontal  for  convenience  only], 

Then  in  (c) 


(20) 


Proof.  —  The  ordinates  to  the  equilibrium  polygon  in  (c)  are  pro- 
portional to  the  ordinates  to  the  true  elastic  curve  of  the  beam  in  (b), 
when  it  is  loaded  with  a  given  load  at  2. 

Now  in  (e),  Fig.  9,  if  the  deflection  at  2  due  to  a  load  P  at  I  is  d, 
then  if  the  load  P  be  moved  to  2,  the  deflection  at  I  will  be  d.  This 
is  known  as  Maxwell's  Theorem,  and  is  proved  as  follows. 

Maxwell's  Theorem.  —  Maxwell's  Theorem  is  "  In  a  beam  if  a  load 
P  be  placed  at  I,  and  the  deflection  A2  of  the  beam  due  to  the  load  be 
measured  at  2,  (a),  Fig.  9a,  then  if  the  load  P  be  placed  at  2,  (b),  and 
the  deflection  Ax  be  measured  at  i,  then  A1  =  A2." 

Proof.  —  Let  the  load  P  be  gradually  applied  at  point  I  (c),  Fig.  9a, 
and  the  work  on  the  beam  will  be  rri  =  JP-81  and  the  deflection  at  2 
will  be  A2.  Then  if  a  load  P  be  applied  gradually  at  point  2,  the  deflec- 
tion at  I  will  be  A1?  (e),  Fig.  9a,  and  the  work  due  to  both  loads  will  be 

W  =  JP-81  +  P-A1  +  JP.82  (2ia) 

Xow  in  (d),  Fig.  9a,  let  P  be  gradually  applied  at  I,  producing  a 
deflection  Ax  at  I,  and  the  work  on  the  beam  will  be  Wz  =  JP-S2.  Then 
if  load  P  be  applied  at  point  I  in  (f),  Fig.  9a,  the  deflection  at  point  2 
will  be  A2,  and  the  work  due  to  both  loads  will  be 

rf'  =  4P.81  +  JP-82  +  P.A2  (2ib) 

Xow  the  work  due  to  both  loads  will  be  independent  of  the  order 
13 


1/2 


MAXWEU/S  THEOREM. 


of  the  application  of  the  loads,  and  equating   (2ia)   and   (2ib)   and 
solving  gives  A±  =  A2,  which  proves  the  theorem. 

Now  in  (c),  Fig.  9,  if  the  deflection  due  to  a  load  unity  at  2  is  m 
at  P±,  then  the  deflection  at  2  due  to  a  load  unity  at  Px  will  be  w.     If 


/*  2 


(a) 


(b) 


\     4 


(d) 


FIG.  9a. 

load  R2  is  applied  at  2,  the  work  done  in  making  the  elastic  curve  pass 
through  2  will  be  %R2-c;  while  the  resistance  due  to  a  load  P±  will  be 
JPX  times  the  deflection  at  2  due  to  the  load  Plt  which  is  equal  to  ^P^m. 
In  like  manner  the  resistance  due  to  P2  will  be  \P«-n,  and 


and 


To  find  ^!  take  moments  about  3  in  (a),  Fig.  9,  and 


(20) 


and  from  similar  triangles  in  (c) 

Substituting  the  value  of  R2  from  (20)  in  (22),  we  have 


(19) 


REACTIONS    OF   DRAW    BRIDGES. 


173 


and  since 


(21) 


Uniform  Load. — For  a  uniform  load  on  the  beam  the  areas  of  the 
diagram  covered  by  the  uniform  load  will  be  used  in  the  place  of  the 
ordinates  as  in  Fig.  9  (see  discussion  on  Influence  Diagrams,  Chapter 

K X -*l 


i_ 


X).     For  example  in  Fig.  10  the  reactions  are  given  by  the  following 
formulas : 

'j  —  area  B2) 


_ 

•*    - 


/(area  A  -f  area  B2  +  area 
/(area  €„  —  area  C^ 


(23) 
(24) 


Drazv  Bridge  with  Four  Supports. — To  find  the  reaction  at  R2 
in  Fig.  1 1 ,  proceed  as  follows :  With  a  load  represented  by  the  triangle 
1-2-4,  construct  a  force  polygon  (not  shown)  and  draw  an  equilibrium 
polygon  passing  through  m-n-o-p.  Xow,  with  a  load  represented  by 
the  triangle  1-3-4,  construct  a  force  polygon  (not  shown)  and  draw  an 
equilibrium  polygon  passing  through  m^o-p.  The  method  of  drawing 
an  equilibrium  polygon  through  three  points  is  explained  in  Chapter 
Y,  Fig.  20. 


174 


DEFLECTION  OF  BEAMS. 


C?t                \*z           t  RZ 
---  L,  ---^|«---  £2---*H 


FIG.  ii. 

Then  in  (c),  Fig.  11, 

R2d  =  Pia  +  P2b  — 


and 


(26) 


/^3  may  be  found  in  a  similar  manner  by  drawing  an  equilibrium 
polygon  for  a  load,  1-3-4,  through  point  n. 

When  R2  and  Rs  have  been  obtained,  the  reactions  Rt  and  R±  can 
most  easily  be  obtained  by  algebraic  moments. 

Proof. — With  the  load,  1-2-4,  and  full  line  deflection  curve  we 
have,  as  in  the  case  of  three  supports, 

Rs(d  +  Ji)=^R3k  +  P1(a  +  e)+P2(b  +  f)+Psg        (27) 

And  with  the  load,  1-3-4,  and  dotted  line  deflection  curve  we  have, 
in  like  manner, 


Subtracting  (28)  from  (27)  we  have 


(29) 


which  is  the  equation  of  which  proof  was  required. 


PART  III. 

DESIGN  OF  MILL  BUILDINGS. 


CHAPTER  XVI. 
GENERAL  DESIGN. 

General  Principles. — The  general  dimensions  and  outline  of  a  mill 
building  will  be  governed  by  local  conditions  and  requirements.  The 
questions  of  light,  heat,  ventilation,  foundations  for  machinery,  hand- 
ling of  materials,  future  extensions,  first  cost  and  cost  of  maintenance 
should  receive  proper  attention  in  designing  the  different  classes  of 
structures.  One  or  two  of  the  above  items  often  determines  the  type 
and  general  design  of  the  structure.  Where  real  estate  is  high,  the  first 
cost,  including  the  cost  of  both  land  and  structure,  causes  the  adoption 
in  many  cases  of  the  multiple  story  building,  while  on  the  other  hand 
where  the  site  is  not  too  expensive  the  single  story  shop  or  mill  is 
usually  preferred.  In  coal  tipples  and  shaft  houses  the  handling  of 
materials  is  the  prime  object;  in  railway  shops  and  factories  turning 
out  heavy  machinery  or  a  similar  product,  foundations  for  the  ma- 
chinery required,  and  convenience  in  handling  materials  are  most  im- 
portant ;  while  in  many  other  classes  of  structures  such  as  weaving 
sheds,  textile  mills,  and  factories  which  turn  out  a  less  bulky  product 
with  light  machinery,  and  which  employ  a  large  number  of  men,  the 
principal  items  to  be  considered  in  designing  are  light,  heat,  ventilation 
and  ease  of  superintendence. 


176  GENERAL  DESIGN 

Shops  and  factories  are  preferably  located  where  transportation 
facilities  are  good,  land  is  cheap  and  labor  plentiful.  Too  much  care 
cannot  be  used  in  the  design  of  shops  and  factories  for  the  reason  that 
defects  in  design  that  cause  inconvenience  in  handling  materials  and 
workmen,  increased  cost  of  operation  and  maintenance  are  permanent 
and  cannot  be  removed. 

The  best  modern  practice  inclines  toward  single  floor  shops  with 
as  few  dividing  walls  and  partitions  as  possible.  The  advantages  of 
this  type  over  multiple  story  buildings  are  (i)  the  light  is  better,  (2) 
ventilation  is  better,  (3)  buildings  are  more  easily  heated,  (4)  founda- 
tions for  machinery  are  cheaper,  (5)  machinery  being  set  directly  on 
the  ground  causes  no  vibrations  in  the  building,  (6)  floors  are  cheaper, 

(7)  workmen  are  more  directly  under  the  eye  of  the  superintendent, 

(8)  materials  are  more  easily  and  cheaply  handled,  (9)  buildings  admit 
of  indefinite  extension  in  any  direction,   ( 10)  the  cost  of  construction 
is  less,  and  (n)  there  is  less  danger  from  damage  due  to  fire. 

The  walls  of  shops  and  factories  are  made  (i)  of  brick,  stone,  or 
concrete;  (2)  of  brick,  hollow  tile  or  concrete  curtain  walls  between 
steel  columns;  (3)  of  expanded  metal  and  plaster  curtain  walls  and 
glass;  (4)  of  concrete  slabs  fastened  to  the  steel  frame;  and  (5)  of 
corrugated  iron  fastened  to  the  steel  frame. 

The  roof  is  commonly  supported  by  steel  trusses  and  framework, 
and  the  roofing  may  be  slate,  tile,  tar  and  gravel  or  other  composition, 
tin  or  sheet  steel,  laid  on  board  sheathing  or  on  concrete  slabs,  tile  or 
slate  supported  directly  on  the  purlins,  or  corrugated  steel  supported  on 
board  sheathing  or  directly  on  the  purlins.  Where  the  slope  of  the  roof 
.is  flat  a  first  grade  tar  and  gravel  roof,  or  some  one  of  the  patent  com- 
position roofs  is  used  in  preference  to  tin,  and  on  a  steep  slope  slate  is 
commonly  used  in  preference  to  tin  or  tile.  Corrugated  steel  roofing 
is  much  used  on  boiler  houses,  smelters,  forge  shops,  coal  tipples,  and 
similar  structures. 

Floors  in  boiler  houses,  forge  shops  and  in  similar  structures  are 
generally  made  of  cinders ;  in  round  houses  brick  floors  on  a  gravel  or 


DETAILS  OF  DESIGN  .  177 

concrete  foundation  are  quite  common;  while  in  buildings  where  men 
have  to  work  at  machines  the  favorite  floor  is  a  wooden  floor  on  a  foun- 
dation of  cinders,  gravel,  or  tar  concrete.  Where  concrete  is  used  for 
the  foundation  of  a  wooden  floor  it  should  be  either  a  tar  or  an  asphalt 
concrete,  or  a  layer  of  tar  should  be  put  on  top  of  the  cement  concrete 
to  prevent  decay.  Concrete  or  cement  floors  are  used  in  many  cases 
with  good  results,  but  they  are  not  satisfactory  where  men  have  to 
stand  at  benches  or  machines.  Wooden  racks  on  cement  floors  remove 
the  above  objection  somewhat.  Where  rough  work  is  done,  the  upper 
or  wearing  surface  of  wooden  floors  is  often  made  of  yellow  pine  or  oak 
plank,  while  in  the  better  classes  of  structures,  the  top  layer  is  com- 
monly made  of  maple.  For  upper  floors  some  one  of  the  common  types 
of  fireproof  floors,  or  as  is  more  common  a  heavy  plank  floor  supported 
on  beams  may  be  used. 

Care  should  be  used  to  obtain  an  ample  amount  of  light  in  build- 
ings in  which  men  are  to  work.  It  is  now  the  common  practice  to  make 
as  much  of  the  roof  and  side  walls  of  a  transparent  or  translucent  ma- 
terial as  practicable ;  in  many  cases  fifty  per  cent  of  the  roof  surface  is 
made  of  glass,  while  skylights  equal  to  twenty-five  to  thirty  per  cent 
of  the  roof  surface  are  very  common.  Direct  sunlight  causes  a  glare, 
and  is  also  objectionable  in  the  summer  on  account  of  the  heat.  Where 
windows  and  skylights  are  directly  exposed  to  the  sunlight  they  may 
best  be  curtained  with  white  muslin  cloth  which  admits  much  of  the 
light  and  shades  perfectly.  The  "saw  tooth"  type  of  roof  with  the 
shorter  and  glazed  tooth  facing  the  north,  gives  the  best  light  and  is 
now  coming  into  quite  general  use. 

Plane  glass,  wire  glass,  factory  ribbed  glass,  and  translucent  fabric 
are  used  for  glazing  windows  and  skylights.  Factory  ribbed  glass 
should  be  placed  with  the  ribs  vertical  for  the  reason  that  with  the  ribs 
horizontal,  the  glass  emits  a  glare  which  is  very  trying  on  the  eyes  of 
the  workmen.  .  \Vire  netting  should  always  be  stretched  under  sky- 
lights to  prevent  the  broken  glass  from  falling  down,  where  wire  glass 
is  nof  used. 


178  GENERAL  DESIGN 

Heating  in  large  buildings  is  generally  done  by  the  hot  blast  sys- 
tem in  which  fans  draw  the  air  across  heated  coils,  which  are  heated 
by  exhaust  steam,  and  the  heated  air  is  conveyed  by  ducts  suspended 
from  the  roof  or  placed  under  the  ground.  In  smaller  buildings,  direct 
radiation  from  steam  or  hot  water  pipes  is  commonly  used. 

The  proper  unit  stresses,  minimum  size  of  sections  and  thickness 
of  metal  will  depend  upon  whether  the  building  is  to  be  permanent  or 
temporary,  and  upon  whether  or  not  the  metal  is  liable  to  be  subjected 
to  the  action  of  corrosive  gases.  For  permanent  buildings  the  author 
would  recommend  16,000  Ibs.  per  square  inch  for  allowable  tensile,  and 

16,000  —  70  — Ibs.  per  square  inch  for  allowable  compressive  stress  for 

direct  dead,  snow  and  wind  stresses  in  trusses  and  columns ;  /  being 
the  center  to  center  length  and  r  the  radius  of  gyration  of  the  member, 
both  in  inches.  For  wind  bracing  and  flexural  stresses  in  columns  due 
to  wind,  add  25  per  cent  to  the  allowable  stresses  for  dead,  snow  and 
wind  loads.  For  temporary  structures  the  above  allowable  stresses  may 
be  increased  20  to  25  per  cent. 

The  minimum  size  of  angles  should  be  2"  x  2"  x  %",  and  the 
minimum  thickness  of  plates  J4",  for  both  permanent  and  temporary 
structures.  Where  the  metal  will  be  subjected  to  corrosive  gases  as  in 
smelters  and  train  sheds,  the  allowable  stresses  should  be  decreased  20 
to  25  per  cent,  and  the  minimum  thickness  of  metal  increased  25  per  cent, 
unless  the  metal  is  fully  protected  by  an  acid-proof  coating  (at  present 
the  best  paints  do  little  more  in  any  case  than  delay  and  retard  the 
corrosion). 

The  minimum  thickness  of  corrugated  steel  should  be  No.  20 
gage  for  the  roof  and  No.  22  for  the  sides ;  where  there  is  certain  to 
be  no  corrosion  Nos.  22  and  24  may  be  used  for  the  roof  and  sides 
respectively. 

The  different  parts  of  mill  buildings  will  be  taken  up  and  discussed 
at  some  length  in  the  following  chapters. 


CHAPTER  XVII. 
FRAMEWORK. 

Arrangement. — The  common  methods  of  arranging  the  frame- 
work in  simple  mill  buildings  are  shown  in  Fig.  i,  Fig.  81  and  Fig.  82. 
The  different  terms  which  are  used  in  the  discussion  that  follows  will 
be  made  clear  by  an  inspection  of  Fig.  I  and  Fig.  81. 


LCo/umn^t  ^£a*tSlruf.  "4-LCotumn 


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jjjpp  "-^ 

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£          £ 

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H  'x\  — 

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(V  '             N 

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v 

"~&rt   -_ 

XN 

Sde    Elevortion 


.^1 


^     / 


Plan  Lower  Chord          Plan  Upper  Chord 

FIG.  81. 

The  three  types  of  mill  buildings — steel  frame  mill  buildings,  mill 
buildings  with  masonry  filled  walls,  and  mill  buildings  with  masonry 
walls — have  been  discussed  in  the  Introduction. 

The  end  post  bent,  shown  in  (a)  Fig.  I  and  in  Fig.  81,  usually  requires 
less  material  than  the  end  trussed  bent  shown  in  (b)  Fig.  I  and  in  Fig. 


i8o 


FRAMEWORK 


82,  and  is  commonly  used  for  simple  mill  buildings.  Extensions  can 
be  made  with  about  equal  ease  in  either  case,  and  the  choice  of  methods 
will  usually  be  determined  by  the  local  conditions  of  the  problem  and 


T       ys^F=isR  r-Ti?cr  0*,*-  *» 


FIG.  82.  A.  T.  &  S.  F.  R.  R.  BLACKSMITH  SHOP,  TOPEKA,  KAS. 

the  fancy  of  the  designer.  In  train  sheds  and  similar  structures  the 
end  trussed  bent  (b),  Fig.  I,  is  used.  Where  the  truss  span  is  quite 
long,  as  in  train  sheds,  the  end  trusses  are  often  designed  for  lighter 
loads  than  are  the  intermediate  trusses,  thus  saving  considerable  ma- 
terial. In  the  case  of  simple  mill  buildings  of  moderate  size  all  trusses 
are,  however,  commonly  made  alike,  the  extra  cost  of  detailing  being 
usually  more  than  the  amount  saved  in  material. 

In  train  sheds,  coliseums,  and  similar  structures  requiring  a  large 
floor  space,  the  three-hinged  arch  is  very  often  used  in  place  of  the 
typical  transverse  bent  system. 

The  various  parts  of  the  framework  of  mill  buildings  will  be  taken 
up  and  discussed  in  order. 

TRUSSES.— Types  of  Trusses.— The  proper  type  of  roof  truss 
to  use  in  any  particular  case  will  depend  upon  the  span,  clear  headroom, 
style  of  truss  preferred,  and  other  conditions.  For  spans  up  to  about 
100  feet,  the  Fink  type  of  truss  is  commonly  used.  This  type  of  truss 
has  the  advantage  of  short  struts,  simplicity  of  details  and  economy. 
The  stresses  that  control  the  design  are  with  but  a  very  few  exceptions 


TYPES  OF  TRUSSES  181 

those  caused  by  an  equivalent  uniform  dead  load,  thus  simplifying  the 
calculation  of  stresses  (see  Table  VI). 

The  outline  of  the  truss  will  depend  upon  the  spacing  of  the  pur- 
lins, and  upon  whether  or  not  the  purlins  are  placed  at  the  panel  points 
of  the  truss.  The  most  economical  and  pleasing  arrangement  is  to 
make  a  panel  point  in  the  truss  under  each  purlin.  Taking  the  normal 
wind  load  on  the  roof  at  from  25  to  30  Ibs.  per  sq.  ft.,  it  will  be  seen 
in  Fig.  112  that  for  Nos.2o  and  22  corrugated  steel,  when  used  without 
sheathing,  the  purlins  should  be  spaced  from  4  to  5  feet.  If  this  spac- 
ing is  exceeded  corrugated  steel  roofing  supported  directly  on  the  pur- 
lins is  almost  certain  to  leak.  Where  sheathing  is  used  the  purlin  spac- 
ing can  be  made  greater.  Many  designers,  however,  pay  no  attention 
to  the  matter  of  placing  the  purlins  at  the  panel  points,  the  upper  chord 
of  the  truss  being  stiffened  to  take  the  flexural  stress. 

In  Fig.  83,  (a)  shows  the  form  of  a  Fink  truss  for  a  span  of  30 
feet;  (b)  for  a  span  of  40  feet;  (c)  for  a  span  of  50  feet-;  (d)  for  a 
span  of  60  feet ;  and  (e)  for  a  span  of  80  feet,  on  the  assumption  that  the 
purlins  are  spaced  from  4  to  5  feet,  and  come  at  the  panel  points  of 
the  truss.  If  trusses  with  vertical  posts  are  desired  the  triangular 
trusses  (h)  and  (j),  or  Fink  truss  (f)  may  be  used.  The  truss  shown 
in  (i)  is  occasionally  used  for  long  spans,  although  it  has  little  to  rec- 
,ommend  it  except  novelty.  The  truss  shown  in  (k)  is  used  where 
there  is  ample  headroom.  The  quadrangular  truss  shown  in  (1)  and 
the  camels  back  truss  shown  in  (m),  are  used  for  long  spans  where  the 
appearance  of  the  truss  is  an  important  feature,  as  in  convention  halls 
and  train  sheds.  The  lower  chords  of  mill  building  trusses  are  usually 
made  horizontal,  but  by  giving  the  lower  chord  a  camber,  as  in  (g),  the 
appearance  from  the  side  is  greatly  improved. 

The  "saw  tooth"  or  "weaving  shed"  roof  shown  in  (a)  Fig.  84, 
has  been  used  abroad  for  many  years  and  is  now  coming  into  quite 
general  use  in  this  country  for  shops  and  factories  as  well  as  for  weav- 
ing sheds,  as  indicated  by  the  name.  The  short  leg  of  the  roof  is  made 
inclined  as  in  (a),  or  vertical  as  in  (b),  and  is  glazed  with  glass  or 


lS2 


FRAMEWORK 


translucent  fabric.  The  glazed  leg  of  the  roof  is  made  to  face  the 
north,  thus  giving  a  constant  and  agreeable  light  and  doing  away  with 
the  use  of  window  shades. 

The  principal  difficulty  in  saw  tooth  roof  construction  is  in  obtain- 


to;  -30  Ft  Span 


(b)  40  Ft  Span 


^v  i  v^ 


(c)   50  Ft- Span 


(d)  60  Ft  Span 


(e)  80  FT  Span 


(f)  Modified  Fink  (g)  Cambered  Fink 

FINK   TRUSSES 


h )     Howe 


f  j  )  Pratt 


(i)    Hybna 


(k)  Modified  Pratt 


(I)    Quadrangular  (m)  Camels  Back 

FIG.  83.    TYPES  OF  ROOF  TRUSSES. 


SAW  TOOTH  ROOF  183 

ing  satisfactory  and  efficient  gutters,  and  in  preventing  condensation 
on  the  inner  surface  of  the  glass  and  gutters.  Another  objection  to  the 
use  of  saw  tooth  roofs  in  localities  having  a  heavy  snowfall  is  that  the 
snow  drifts  the  roof  nearly  full  and  shuts  off  the  light.  The  common 
method  of  preventing  the  snow  from  collecting,  and  for  taking  care  of 
the  roof  water,  is  that  given  in  the  description  of  the  Conkey  plant, 
which  see. 

The  modified  saw  tooth  roof  shown  in  (b),  Fig.  84,  is  pro- 
posed by  the  author  as  a  substitute  for  the  usual  type  of  saw  tooth 
roof  shown  in  (a).  This  modified  saw  tooth  roof  allows  the  use  of 
ordinary  valley  gutters,  and  gives  an  opportunity  to  take  care  of  the 
condensation  on  the  inner  surface  of  the  glass  by  suspending  a  gutter 
at  the  bottom  of  the  monitor  leg.  Snow  will  cause  very  little  trouble 

South  End  North  End 


(d)   Saw  Tooth    ( Weaving  Shed) 


South  End  North  End 

-q'ass 

-> 


Cb)  Modified  Saw  Tooth 
FIG.  84. 

with  this  roof  on  account  of  the  increased  depth  of  gutter.  The  mod- 
ified saw  tooth  roof  has  a  greater  pitch,  and  has  a  more  economical  truss 
for  long  spans  than  the  common  form  shown  in  (a).  Condensation  on 
the  inner  surface  of  the  glazed  leg  can  be  practically  prevented  by  us- 
ing double  glazing  with  an  air  space  between  the  sheets  of  glass.  Double 


1 84  FRAMEWORK 

glazing  in  windows  and  skylights  makes  the  building  much  easier  to 
heat,  the  air  space  making  an  almost  perfect  non-conductor. 

Brown  &  Sharp e  Foundry. — In  the  Brown  &  Sharpe  Mfg.  Com- 
pany's Foundry,  a  modification  of  the  saw  tooth  roof  was  adopted  in 
which  glass  was  used  on  both  surfaces  of  the  roof.  The  skylights  ex- 
tend east  and  west  and  have  a  pitch  of  45  degrees.  The  southerly  pitch 
is  glazed  with  opaque  glass,  the  other  with  ordinary  rough  glass.  The 
ventilator  monitor,  which  surmounts  the  skylights,  is  glazed  with  opaque 
glass  on  the  southerly  side,  and  extends  high  enough  so  that  no  light 
up  to  an  angle  of  70  degrees  reaches  the  glass  below.  By  this  arrange- 
ment no  direct  sunlight  is  admitted  to  the  shop  from  above  excepting 
for  a  few  minutes  at  noon  during  the  longest  days  of  the  year.  The 
result  of  this  overhead  light,  combined  with  the  almost  wholly  glass 
walls  of  the  room  is  that  the  floor  below  is  as  light  as  out  of  doors,  to 
all  intents  and  purposes,  yet  diffused  light  only  is  admitted.  A  rod 
placed  upright  on  the  floor  of  one  of  these  rooms  casts  no  shadow. 

Conkey  Printing  Plant*. — The  printing  plant  of  the  W.  B.  Conkey 
Co.,  Hammond,  Ind.,  consists  of  a  single  story  building,  540x450  ft. 
The  roof  is  of  the  weaving  shed  or  saw  tooth  type  and  all  windows 
are  glazed  with  frosted  glass  and  are  placed  at  an  angle,  looking  toward 
the  north.  Every  29  feet  of  roof  space  provides  1 1  feet  of  light.  Ow- 
ing to  the  angle  of  the  roof  the  direct  rays  of  light  are  kept  out  of  the 
building,  which  is  thus  lighted  by  the  soft  reflected  rays  from  the 
northern  sky.  The  entire  roof  is  built  up  out  of  light  structural  steel- 
work resting  on  cast  iron  columns  spaced  29  ft.  c.  to  c.  one  way,  and  16 
ft.  c.  to  c.  in  the  other  direction.  The  height  of  the  trusses  above  the 
floor  is  12  ft.  To  prevent  the  snow  collecting  in  the  valleys  between 
the  skylights,  the  bottom  of  the  gutter  and  the  glass  are  kept  heated  so 
that  the  snow  melts  as  it  falls.  This  method  produces  condensation  on 
the  inner  surface  of  the  glass,  which  is  collected  in  a  system  of  con- 
densation gutters  and  carried  outside  the  building. 

The  heating  and  ventilating  of  the  building  is  accomplished  by  a 
blast  system,  with  the  heating  ducts  under  the  floor,  which  supply  reg- 
isters throughout  the  plant,  arranged  on  the  side  walls  of  each  depart- 
ment. The  heating  system  can  be  made  to  produce  a  mild  heat  for  the 
seasons  of  spring  and  fall,  and  can  also  be  turned  into  a  cooling  sys- 
tem in  the  summer,  by  running  cold  water  through  the  steam  pipes  at 

•Engineering  News,  Dec.  8,  1898. 


SAW  TOOTH  ROOFS  185 

the  fan  and  changing  the  air  every  15  minutes  with  cool  air  in  hot 
weather. 

The  floor  is  built  of  heavy  plank  and  finished  maple  laid  on  sleep- 
ers which  are  bedded  in  cinders.  The  walls  are  made  of  heavy  tile  and 
the  openings  are  closed  with  iron  fire  doors.  The  building  is  practically 
fireproof  and  takes  a  very  low  rate  of  insurance. 

Boyer  Plant. — The  Boyer  Plant  of  the  Chicago  Pneumatic  Tool 
Co.,  at  Detroit,  Mich.,  is  325  x  185  ft.,  with  the  longer  dimension  ex- 
tending north  and  south.  The  roof  of  the  building  is  divided  into  two 
sections,  having  spans  of  about  92  ft.  each,  a  pitch  of  about  ^4,  and  is 
covered  with  Patent  Asbestos  Roofing — manufactured  by  H.  W.  Johns- 
Manville  Co.,  Milwaukee,  Wis. — laid  on  i^-in.  plank  sheathing.  The 
building  is  lighted  by  means  of  saw  tooth  skylights  facing  north  and 
extending  from  the  ridge  of  the  roof  to  within  about  6  ft.  of  the  eaves 
on  the  outside  and  the  valley  gutter  on  the  inside.  The  trusses  are 
spaced  16  ft.  apart,  and  there  are  three  saw  tooth  skylights  between  each 
pair  of  trusses,  making  240  skylights  in  the  roof.  The  north  leg  of 
the  saw  tooth  is  vertical  and  is  glazed  with  double  corrugated  glass, 
the  south  leg  is  covered  with  asbestos  roofing.  The  building  is  venti- 
lated by  means  of  circular  ventilators  placed  in  the  ridge  of  the  roof 
and  spaced  16  ft.  apart.  The  lighting  in  this  building  is  almost  perfect. 
The  roofing  has  given  satisfaction  with  the  exception  of  the  large  val- 
ley gutters,  which  will  be  covered  with  copper  or  lead  in  the  near 
future.  There  has  been  a  little  trouble  with  condensation,  but  not 
enough  to  make  it  necessary  to  go  to  the  expense  of  putting  in  con- 
densation gutters. 

This  building  is  described  in  the  Railway  and  Engineering  Review, 
March  9,  1901. 

For  additional  details  of  saw  tooth  roofs  see  Fig.  97. 

The  cross-section  of  a  locomotive  shop  for  the  Eastern  Railway 
of  France  is  shown  in  Fig.  85.  The  entire  building  is  made  of  fireproof 
materials,  the  framework  is  of  iron  and  the  roof  of  sheet  metal  and 
glass.  The  building  extends  from  east  to  west  and  has  a  saw  tooth  roof, 
with  the  shorter  leg  facing  north,  and  glazed  with  crinkled  glass.  The 
floor  is  made  of  treated  oak  cubes  measuring  3.94  in.  on  the  edge,  set 
with  the  grain  vertical,  on  a  bed  of  river  sand  about  8  in.  thick.  The 
saw  tooth  roof  is  well  suited  to  structures  of  this  class. 


i86 


FRAMEWORK 


Example  of  Ketchum's  Modified  Saw  Tooth  Roof. — The  modified 
form  of  saw  tooth  roof  described  above  was  proposed  by  the  author 
in  the  first  edition  (1903).  This  form  of  saw  tooth  roof  has  recently 
(1905)  been  used  in  the  paint  shops  of  the  Plank  Road  Shops  of  the 
Public  Service  Corporation  of  New  Jersey,  Newark,  N.  J.  The  build- 
ing proper  is  135  feet  wide  by  354  feet  long.  The  main  trusses  are  of 
the  modified  saw  tooth  type  with  44- ft.  spans  and  a  rise  of  J4,  and  are 
spaced  16  ft.  centers.  The  general  details  of  one  of  the  main  trusses 
are  shown  in  Fig.  84a. 

The  building  has  an  independent  steel  framing  with  brick  curtain 
walls  on  the  exterior.  Pilasters  24  in.  by  20  in.  are  placed  16  feet  apart 
under  the  ends  of  the  trusses,  the  intermediate  curtain  walls  being 
12  inches  thick. 

The  roof  is  a  5 -ply  slag  roof  laid  on  2-in.  tongued  and  grooved 
spruce  sheathing,  which  is  spiked  to  2  in.  X  5  in.  spiking  strips,  which 
are  bolted  to  8-in.  channel  purlins  spaced  6  feet  centers.  The  slag 
roofing  is  laid  to  comply  with  standard  specifications  as  described  in 
Part  IV. 


fin  Portland  Cement  Finish. 
•/  Finished  Floor  Level 


12  C/ndeyy 
-4*  1 : 3 :5  Portland  Cement  Concrete 


Stone 
Base, 
-?*&$' 


FIG.  84a.    MODIFIED  SAW  TOOTH  ROOF,  PAINT  SHOP,  PUBLIC  SERVICE 

CORPORATION. 


SAW  TOOTH  ROOFS 


187 


The  roof  water  is  carried  down  5-111.  cast  iron  leaders  attached  to 
alternate  interior  columns. 

The  sash  in  the  vertical  leg  are  in  two  rows,  the  upper  row  being 
hinged  at  their  centers,  thus  providing  ample  ventilation.  Condensation 
gutters  are  placed  below  the  vertical  leg  to  take  the  drip.  The  skylight 
area  is  about  20  per  cent  of  the  roof  area,  the  window  area  is  about 
45  per  cent  of  the  outside  walls,  while  about  28  per  cent  of  the  entire 
outside  surface  of  the  building  is  of  glass.  All  glazing  is  of  }^-in. 
ribbed  wire  glass,  with  the  ribs  placed  vertical. 

The  skylight  frames  and  moldings  are  made  of  No.  24  galvanized 
iron,  while  the  entire  roof  is  flashed  with  i6-oz.  copper  sheets,  4  feet 
wide,  and  counter  flashed  with  sheet  lead. 

Louisville  &  Nashville  R.  R.  Shops. — The  saw  tooth  roof  shown 
in  Fig.  84b  was  used  in  the  South  Louisville  shops  of  the  Louisville 
&  Xashville  R.  R.  The  roof  covering  is  composed  of  composition 
roofing  on  the  pitched  roof  and  asphalt  and  gravel  roofing  on  the 
flat  portions  laid  on  ij4"  dressed  and  matched  sheathing. 


FIG.  84b.    SAW  TOOTH  ROOF,  LOUISVILLE  &  NASHVILLE  R.  R.  SHOPS. 

The  short  leg  of  the  saw  tooth  is  glazed  with  ribbed  wire  glass, 
and  the  building  is  ventilated  by  means  of  12-inch  circular  ventilators 
placed  in  the  peak  of  the  saw  teeth  and  spaced  30'  2". 

Saw  Tooth  Roof  of  the  Ingersoll-S argent  Drill  Co. — The  design 
of  the  saw  tooth  roof  used  on  the  Rock  Drill  building  is  shown  in  Fig. 
84c.  The  floors  are  of  concrete  and  the  roof  is  of  reinforced  concrete 
covered  with  felt  and  slag.  Ribbed  glass  is  used  in  the  glazed  tooth. 
It  will  be  noticed  that  electric  motors  for  driving  the  machinery  are 


1 88 


FRAMEWORK 


placed  on  small  platforms  resting  on  the  lower  chords  of  the  roof 
trusses. 


Copper  Copmg-. 


FIG.  84c.    SAW  TOOTH  ROOF  FOR  ROCK  DRILL  BUILDING.* 

Erecting  and  Machine  Shop  of  P.  &  L.  E.  R.  R. — The  locomotive- 
erecting  and  machine  shop  of  the  P.  &  L.  E.  R.  R.,  at  McKees  Rocks 
is  533'  X  1 68'  i",  and  is  designed  with  a  self-supporting  frame  with 
brick  curtain  walls. 

The  details  of  the  roof  are  shown  in  the  cross-section  in  Fig.  84d, 
the  machine  shop  being  well  lighted  by  three  saw  tooth  windows.  The 
roofing  is  asphalt  and  felt  laid  on  \y%"  tongued  and  grooved  boards. 
The  gutters  are  heavily  flashed  with  asphalt  and  felt.  The  roof  water 
in  the  saw  tooth  part  is  carried  by  4"  conductors  to  5"  vertical  discharge 
pipes,  attached  to  alternate  columns  (40  ft.  apart)  as  shown.  The  de- 
tails of  the  saw  tooth  windows  are  given  in  Fig.  i57a.  The  floors  have 
a  1-3-5  Portland  cement  concrete  base  4"  thick,  on  this  are  placed 
five  layers  of  felt  saturated  with  asphalt  for  waterproofing.  This  is 
covered  with  a  layer  of  dry  sand  about  5"  thick  and  the  4"  X  3%" 
floor  stringers  are  well  bedded  in  the  sand.  The  wearing  floor  con- 
sists of  a  sub-floor  of  2%"  yellow  pine  and  a  top  floor  of  \y%"  tongued 
and  grooved  maple.  Wire  boxes  are  put  in  as  shown  in  Fig.  84d  to 
carry  power  and  light  wires. 

*  Engineering  News,  June  20,  1905. 


SAW  TOOTH  ROOFS 


189 


190 


FRAMEWORK 


56-5 


-121-4- 


FIG.  85.    LOCOMOTIVE  SHOP,  EASTERN  RAILWAY  OF  FRANCE. 

A  few  of  the  forms  of  trusses  in  common  use  where  ventilation 
and  light  are  provided  for  are  shown  in  Fig.  86.    The  Fink  truss  with 


gloss  or  louvres 
glass 
glass  or  louvres 


(a) 


(b) 


glass  -^X|\<- glass 


glass-Z_i 


(C) 


glass  or  louvres 
gloss 


(d 


circufar  ventilator 


glass 


<3lass  glass 


(q) 


glass 


FIG.  86. 


(h)  Silk  Mill 


PITCH  OF  ROOF  191 

monitor  ventilator  and  skylights  in  the  roof  shown  in  (a),  is  a  favorite 
tvpe  for  shops;  truss  (b)  with  double  monitor  ventilator  is  especially 
adapted  to  round  house  construction;  trusses  (c)  and  (e)  are  adapted: 
to  shop  and  factory  construction  where  a  large  amount  of  light  is  de- 
sired, ventilation  being  obtained  by  means  of  circular  ventilators ;  truss 
(d)  is  similar  to  (c)  and  (e),  but  allows  of  better  ventilation;  truss  (f) 
has  skylights  in  the  roof  and  has  circular  ventilators  placed  along  the 
ridge  of  the  roof;  truss  (g)  is  the  type  in  common  use  for 
blacksmith  shops,  boiler  houses,  and  roofs  of  small  span.  The  "silk 
mill"  roof  shown  in  (h)  was  used  by  the  Klots  Throwing  Co.  in  their 
silk  mill  at  Carbondale,  Pa.  The  spans  of  the  three  trusses  are  48'  8" 
each,  with  a  clerestory  of  13'  9"  in  the  monitor  ventilators,  which  are 
glazed  with  glass  n'  o"  high.  The  monitors  face  east  and  west,  al- 
lowing a  maximum  amount  of  direct  sunlight  in  the  morning  and 
evening,  and  none  at  midday.  This  roof  has  given  very  satisfactory 
results,  however,  it  would  seem  to  the  author  that  it  would  be  necessary 
to  use  shades,  and  that  there  would  be  shadows  in  the  building.  The 
trusses  in  this  building  are  spaced  10'  6"  apart  and  support  the 
plank  sheathing  which  carries  the  roof,  no  purlins  being  used.  The 
shafting  to  run  the  machinery  in  this  building  is  placed  in  a  sub-base- 
ment ;  a  method  much  more  economical  and  convenient  than  the  com- 
mon one  of  suspending  the  shafting  from  the  trusses. 

Pitch  of  Roof. — The  pitch  of  a  roof  is  given  in  terms  of  the  center 
height  divided  by  the  span;  for  example  a  6o-ft.  span  truss  with  y± 
pitch  will  have  a  center  height  of  15  ft.  The  minimum  pitch* allow- 
able in  a  roof  will  depend  upon  the  character  of  the  roof  covering,  and 
upon  the  kind  of  sheathing  used.  For  corrugated  steel  laid  directly  on 
purlins,  the  pitch  should  preferably  be  not  less  than  y±  (6"  in  12"),  and 
the  minimum  pitch,  unless  the  joints  are  cemented,  not  less  than  Y$. 
Slate  and  tile  should  not  be  used  on  a  less  slope  than  l/+  and  preferably 
not  less  than  l/$.  The  lap  of  the  slate  and  tile  should  foe  greater  for  the 
less  pitch.  Gravel  should  never  be  used  on  a  roof  with  a  greater  pitch 
than  about  J^ ,  and  even  then  the  composition  is  very  liable  to  run.  As- 


192  FRAMEWORK 

phalt  is  inclined  to  run  and  should  not  be  used  on  a  roof  with  a  pitch 
of  more  than,  say,  2  inches  to  the  foot.  If  the  laps  are  carefully  made 
and  cemented  a  gravel  and  tar  or  asphalt  roof  may  be  practically  flat ;  a 
pitch  of  24  to  i  inch  to  the  foot  is,  however,  usually  preferred.  Tin 
may  be  used  on  a  roof  of  any  slope  if  the  joints  are  properly  soldered. 
Most  of  the  patent  composition  roofings  give  better  satisfaction  if  laid 
on  a  roof  with  a  pitch  of  y$  to  %.  Shingles  should  not  be  used  on  a 
roof  with  a  pitch  less  than  }4>  and  preferably  the  pitch  should  be  J<j 
to  y2. 

Pitch  of  Truss. — There  is  very  little  difference  in  the  weight  of 
Fink  trusses  with  horizontal  bottom  chords,  in  which  the  top  chord 
has  a  pitch  of  y$,  J4,  or  J^.  The  difference  in  weight  is  quite  notice- 
able, however,  when  the  lower  chord  is  cambered;  the  truss  with  the 
Y$  pitch  being  then  more  economical  than  either  the  J^  or  the  %  pitch. 
Cambering  the  lower  chord  of  a  truss  more  than,  say,  1-40  of  the  span 
adds  considerable  to  the  weight.  For  example  the  computed  weights 
of  a  6o-ft.  Fink  truss  with  a  horizontal  lower  chord,  and  a  6o-ft. 
Fink  truss  with  a  camber  of  3  feet  in  the  lower  chord,  showed  that  the 
cambered  truss  weighed  40  per  cent  more  for  the  J4  pitch  and  15  per 
cent  more  for  the  y$  pitch,  than  the  truss  having  the  same  pitch  with 
horizontal  lower  chord.  It  is,  however,  desirable  for  appearance  sake 
to  put  a  slight  camber  in  the  bottom  chords  of  roof  trusses,  for  the 
reason  that  to  the  eye  a  horizontal  lower  chord  will  appear  to  sag  if 
viewed  from  one  side. 

In  deciding  on  the  proper  pitch,  it  should  be  noted  that  while  the 
y$  pitch  gives  a  better  slope  and  has  a  less  snow  load  than  a  roof  with 
y^  or  y$  pitch,  it  has  a  greater  wind  load  and  more  roof  surface.  Tak- 
ing all  things  into  consideration  *4  pitch  is  probably  the  most  econom- 
ical pitch  for  a  roof.  A  roof  with  J^  pitch  is,  however,  very  nearly  as 
economical,  and  should  preferably  be  used  where  corrugated  steel  roof- 
ing is  used  without  sheathing,  and  where  the  snow  load  is  large. 

Economic  Spacing  of  Trusses. — The  weight  of  the  trusses  and 
columns  per  square  foot  of  area  decreases  as  the  spacing  increases,  while 


PITCH  OF  TRUSS 


'93 


the  weight  of  the  purlins  and  girts  per  sqaare  foot  of  area  increases  as 
the  spacing  increases.  The  economic  spacing  of  the  trusses  is  a  func- 
tion of  the  weight  per  square  foot  of  floor  area  of  the  truss,  the  pur- 
lins, 'the  side  girts  and  the  columns,  and  also  of  the  relative  cost  of  each 
kind  of  material.  For  any  given  conditions  the  spacing  which  makes 
the  sum  of  these  quantities  a  minimum  will  be  the  economic  spacing. 
It  is  desirable  to  use  simple  rolled  sections  for  purlins  and  girts,  and 
under  these  conditions  the  economic  spacing  will  usually  be  between  16 
and  25  feet.  The  smaller  value  being  about  right  for  spans  up  to,  say, 
60  feet,  designed  for  moderate  loads,  while  the  greater  value  is  about 
right  for  long  spans,  designed  for  heavy  loads. 


11. 


4'CJf 

j 

!?>   do   * 

* 

[ 
r' 

4--^ 

^  do     ^ 

_    ^ 

s 

, 

TrtsAs 

1 

, 

f 

T. 

i;  ! 

^ 


fc-<y'/// *  *   oi/s 

Part  FraminqPlan 


Section  A-B 

FIG.  87.    STEEL  ROOF  COVERED  WITH  LUDOWICI  TILE. 

• 

Calculations  of  a  series  of  simple  Fink  trusses  resting  on  walls 
and  having  a  uniform  span  of  60  feet,  and  different  spacings  gave  the 
least  weight  per  square  foot  of  horizontal  projection  of  the  roof  for 
a  spacing  of  18  ^eet,  and  the  least  weight  of  trusses  and  purlins  com- 
bined for  a  spacing  of  10  feet.  The  weight  of  trusses  per  square  foot 
was,  however,  more  for  the  lO-ft.  spacing  than  for  the  i8-ft.  spacing, 
so  that  the  actual  cost  of  the  steel  in  the  roof  was  a  minimum  for 'a 


FRAMEWORK 


spacing  of  about  16  feet ;  the  shop  cost  of  the  trusses  per  pound  being 
several  times  that  of  the  purlins.     Local  conditions  and  requirements 


-Glass  or  Louvres 


(a) 


(e) 


-Glass  or  Louvres 


(b) 


^^  Glass 

^ 

*-  Glass  or  Louvres 

czsZSZSZ 

v\7^A7 

f~ 

\ 

(c) 


-Glass 


^ 

'    TrovelinqCrone^ 

toj  loj     J 

<-Gloss 
VV^ 

\ 

x^ 

\ 

(f) 


Glass 


(q) 


id)  (hi 

FIG.  88.    TYPKS  OF  TRANSVERSE  BENTS. 


TRANSVERSE  BENTS. 


usually  control  the  spacing  of  the  trusses  so  that  it  is  not  necessary  that 
we  know  the  economic  spacing  very  definitely. 

For  long  spans  the  economic  spacing  can  be  increased  by  usinsf 
rafters  supported  on  heavy  purlins,  placed  at  greater  distances  than 
would  be  required  if  the  roof  were  carried  directly  by  the  purlins.  This 
method  is  frequently  used  in  the  design  of  train  sheds  and  roofs  of 
buildings  where  plank  sheathing  is  used  to  support  slate  or  tile  cover- 
ings, or  where  the  tiles  are  supported  by  angle  sub-purlins  spaced  close 
together  as  shown  in  Fig.  87. 

TRANSVERSE  BENTS.— The  proper  cross-section  for  a  mill 
building  will  depend  upon  the  use  to  which  the  finished  structure  is  to 


Gravel    Roof- 


Skylight 


75-0"- 4Jc 75-0" 


rr 69-9*- 


/KJ\  I V--Concrete'7 V 

I,  ' Z  ,1  i,.  .  .  i  '  •  •  •  •  •* 

Ttrr  III  HIM 


'50-0" 


400' Long 

Locomotive  Shop- Oregon  Short  [line 
FlG.  89. 

be  put.  A  number  of  the  common  types  of  transverse  bents  are  shown 
in  Fig.  88.  Transverse  bents  (a),  (b),  (d)  and  (h)  are  commonly 
used  for  boiler  houses,  shops  and  small  train  sheds.  Where  a  travel- 
ing crane  is  desired,  the  crane  girders  are  commonly  suspended  from  the 
trusses  in  the  bents  referred  to,  although  the  crane  may  be  made  to 
span  the  entire  building  as  in  (h).  Transverse  bent  (d)  was  used 
for  a  round  house  with  excellent  results.  Transverse  bents  (f)  and  (g) 
are  quite  commonly  used  where  it  is  desired  that  the  main  part  of  the 
building  be  open  and  be  provided  with  a  traveling  crane  that  will  sweep 


196 


FRAMEWORK 


the  building,  while  the  side  rooms  are  used  for  lighter  tools  and  mis- 
cellaneous work.  Transverse  bent  (c)  may  be  used  in  the  same  way 
as  (g),  by  supplying  a  traveling  crane.  Transverse  bent  (e)  is  very 
often  used  for  shops. 

Cross-sections  of  the  locomotive  shops  of  several  of  the  leading 
railways  are  shown  in  Figs.  89  to  92,  inclusive,  and  the  locomotive  shops 
of  the  A.  T.  &  S.  F.,  and  the  Philadelphia  and  Reading  Railroads 
are  described  in  detail  in  Part  IV.  For  the  most  part  these  buildings 


I3T-0 
<5 40'  Long 
Locomotive  Shop  -5t-L-.l-M-&5- 

FIG.  90. 

are  built  with  self-supporting  frames,  and  have  brick  walls  built  out- 
side the  framing.    The  arrangement  of  the  cranes,  provisions  for  light- 


Skylight 


^ 

4<96-0  Long 
Locomotive  Shop -Union  Pacific 

FIG.  91. 


TRUSS  DETAILS 


197 


ing  and  ventilating,  and  the  main  dimensions  are  shown  in  the  cuts  and 
need  no  explanation. 


Locomotive  Shop -AT&  5-F 

FIG.  92. 

A  cross-section  and  end  view  of  the  train  shed  of  the  Richmond 
Union  Passenger  Station  are  shown  in  Fig.  93.     Riveted  trusses  are 


Crns»    Section,    Looking    Piorth.  Elevation,    Xorth    End. 

Train  Shed— Richmond  Union  Passenger  Station. 

FIG.  93. 

quite  generally  used  in  train  sheds ;  a  notable  exception  to  this  state- 
ment, however,  being  the  trusses  for  the  new  train  shed  of  the  C.  R.  I. 
&  P.,  and  L.  S.  &  M.  S.  Railways  in  Chicago.  The  trusses  in  this  struc- 
ture have  a  length  of  span  of  207  ft.,  a  rise  of  the  bottom  chord  of  40  ft. 
and  a  depth  of  truss  at  the  center  of  25  ft.  The  trusses  are  pin  con- 
nected, the  compression  members  being  built  up  channels  and  the  ten- 
sion members  eye-bars.  The  building  is  described  in  detail  in  Engineer- 
ing News,  August  6,  1903. 

Truss  Details. — Riveted  trusses  are  commonly  used  for  mill  build- 
ings and  similar  structures.     For  ordinary  loads,  the  upper  and  lower 


i98 


FRAMEWORK 


chords,  and  the  main  struts  and  ties  are  commonly  made  of  two  angles 
placed  back  to  back,  forming  a  T-section,  the  connections  being  made 
by  means  of  plates.  The  upper  chord  should  preferably  be  made  of 
unequal  legged  angles  with  the  short  legs  turned  out.  Sub-struts  and 
ties  are  usually  made  of  one  angle.  Flats  should  not  be  used.  Where 
a  truss  member  is  made  of  two  angles  placed  back  to  back,  the  angles 
should  always  be  riveted  together  at  intervals  of  2  to  4  feet. 

Trusses  that  carry  heavy  loads  or  that  support  a  traveling  crane 
or  hoist,  are  very  often  made  with  a  lower  chord  composed  of  two  chan- 
nels placed  back  to  back  and  laced  or  battened,  and  are  sometimes  made 
with  channel  chord  sections  throughout  (see  Fig.  175). 

When  the  purlins  are  not  placed  at  the  panel  points  of  the  truss 
the  upper  chord  must  be  designed  for  flexure  as  well  as  for  direct  stress. 
The  section  in  most  common  use  for  the  upper  chord,  where  the  purlins 
are  not  placed  at  the  panel  points,  is  one  composed  of  two  angles  and  a 
plate  as  shown  in  (c)  Fig.  96. 


^L_ 

OOOOOOOQl                      J 

| 

j 

7 

w 

-~ 

(a) 

o  o  o  o  o 


o  o  o  o  o  o  o ; 


(b) 
FIG.  94. 


Trusses  may  be  fastened  to  the  columns  by  means  of  a  plate  as 
shown  in  (a)  Fig.  94,  or  by  means  of  connection  angles  as  shown  in 
(b)  and  (c).  The  first  method  is  to  be  preferred  on  account  of  the 
rigidity  of  the  connection,  and  the  ease  with  which  the  field  connection 
can  be  made. 


TRUSS   DETAILS. 


199 


FIG.  95.     DETAIL  SHOP  PLANS  FOR  A  ROOF  TRUSS. 


200 


FRAMEWORK 


Trusses  supported  directly  on  masonry  walls  have  one  end  sup- 
ported on  sliding  plates  for  spans  up  to  about  70  feet;  for  greater 
lengths  of  span  one  end  should  be  placed  on  rollers,  or  should  be  hung 
on  a  rocker.  Trusses  for  mill  buildings  should  be  made  with  riveted 
rather  than  with  pin  connections,  on  account  of  the  greater  rigidity  of 
the  riveted  structure.  The  complete  shop  drawings  of  a  truss  for  the 
machine  shop  at  the  University  of  Illinois,  are  shown  in  Fig.  95.  This 
truss  is  more  completely  detailed  than  is  customary  in  most  bridge 
shops.  The  practice  in  many  shops  is  to  sketch  the  truss,  giving  main 
dimensions,  number  of  rivets  and  lengths  of  members,  depending  on  the 


(• Span  45'-0' Pitch  30' 

FIG.  96. 


TRUSS  DETAILS  201 

templet  maker  for  the  rest.  In  Fig.  95  the  rivet  gage  lines  are  taken 
as  the  center  lines.  This  is  the  most  common  practice,  although  many 
use  one  leg  of  the  angle  as  the  center  line  in  secondary  members.  The 
latter  method  has  the  advantage  of  reducing  the  length  of  connection 
plates  without  introducing  secondary  stresses  that  are  liable  to  be 
troublesome. 

The  detail  drawings  of  a  transverse  bent  are  shown  in  Fig.  96. 
The  common  methods  of  attaching  purlins  and  girts,  and  of  making 
lateral  connections  are  also  shown.  The  fan  type  of  Fink  Truss  shown 
in  Fig.  96  is  quite  commonly  used  where  an  odd  number  of  panels  is 
desired,  and  makes  a  very  satisfactory  design.  The  details  of  the  end 
connection  of  a  60- ft.  span  truss  are  shown  in  (a),  and  of  a  45-ft.  span 
truss  with  a  reinforced  top  chord  are  shown  in  (c),  Fig.  96.  The 
method  of  reinforcing  the  top  chord  shown  (c)  is  the  one  most  com- 
monly employed  where  purlins  are  not  placed  at  the  panel  points.  The 
method  of  making  lateral  connections  for  the  lateral  rods  shown  in  (c) 
is  not  good,  for  the  reason  that  it  brings  bending  stresses  in  a  plate 
which  is  already  badly  cut  up. 

The  detail  drawings  of  a  saw  tooth  roof  bent  for  the  Mathiessen  & 
Hegeler  Zinc  Works,  LaSalle,  111.,  are  shown  in  Fig.  97.  This  building 
was  erected  in  1899  along  the  lines  suggested  by  an  experience  with  a 
similar  saw  tooth  roof  building  erected  in  1874.  The  building  was  de- 
signed by  Mr.  August  Ziesing,  Vice  President  American  Bridge  Co., 
and  was  erected- by  the  American  Bridge  Co. 

The  following  description  is  from  a  personal  letter  from  Mr.  Julius 
Hegeler  of  the  firm  of  Mathiessen  &  Hegeler,  to  the  author  in  reply  to 
a  request  for  plans:  "The  cast  iron  gutters  are  fastened  to  the  pur- 
lins and  roof  boards  by  spikes  through  holes  in  the  gutters  (holes  are 
not  shown  in  the  drawing)  ;  on  account  of  their  slope,  however,  hardly 
any  fastening  is  necessary.  These  gutters  are  so  placed  that  the  gal- 
vanized iron  down  spouts  are  next  to  the  posts,  there  being  two  down 
spouts  at  each  post.  The  condensation  gutters  are  fastened  to  the  gut- 
ters and  empty  into  the  down  spouts.  Ice  has  never  caused  any  trouble 
by  forming  in  the  gutters." 


202 


FRAMEWORK 


Details  of  COST  Iron  Gutter 


FIG.  97.   CROSS-SECTION  OF  THE  SHOPS  OF  THE  MATHIESSEN  &  HEGELER 
ZINC  WORKS, 


The  original  saw  tooth  roof  shop  built  by  this  firm  in  1874  is  still 
in  use,  and  is  one  of  the  first,  if  not  the  first,  saw  tooth  roofs  built  in 
America. 

COLUMNS. — The  common  forms  of  columns  used  in  mill  build- 
ings are  shown  in  Fig.  98.  For  side  columns  where  the  loads  are  not 
excessive,  column  (g)  composed  of  four  angles  laced  is  probably  the 
best.  In  this  column  a  large  radius  of  gyration  about  an  axis  at  right 
angles  to  the  direction  of  the  wind  is  obtained  with  a  small  amount 


TYPES  OF  MILL  BUILDING  COLUMNS 


203 


of  metal.  The  lacing  should  be  designed  to  take  the  shear,  and  should 
be  replaced  by  a  plate,  (f)  Fig.  98,  where  the  shear  is  excessive,  or 
where  the  bending  moment  developed  at  the  base  of  the  column  requires 
the  use  of  excessive  flanges.  The  I  beam  column  (h)  makes  a  good 
side  column  where  proper  connections  are  made,  and  is  commonly  used 
for  end  columns  (see  Fig.  81).  The  best  corner  column  is  made  of 
an  equal  legged  angle  with  4,  5  or  6-in.  legs,  (i)  Fig.  98.  Details  for 
the  bases  of  the  three  columns  above  described  are  shown  in  Fig.  99. 


i 

m 


l 


2  Channels 

Laced 

(a) 


2  Channels 

Laced 

(b) 


u    n 


2  Channels 

2  Plates 

(C) 


2  Channels 

1 1  Beam 

(d) 


X 

4  Z  Bars 

I  Plate 

Ce) 


4  Angles 

I  Plate 

(f) 


1 1  Beam 
(h) 


H 

Special 
I  Beam 


Larimer  Gray 

(k)  (I) 

15  FlG.  98.     TYPES  OF  MILL  BUILDING  COLUMNS. 


4  Angles 
Box  Laced 
(m) 


O 


4  Angles 

Box  Laced 

(n) 


1 


4  Angles 

Starred 

(O) 


204  FRAMEWORK 

Columns  made  of  two  channels  laced,  or  two  channels  and  two 
plates,  are  used  where  moderately  heavy  loads  are  to  be  carried.  Chan- 
nel column  (a),  with  channels  turned  back  to  back  and  laced,  is  the  form 
most  commonly  used;  column  (b),  with  the  backs  of  the  channels 
turned  out  and  laced,  gives  a  better  chance  to  make  connections  and  can 
be  made  to  enter  an  opening  without  chipping  the  legs  of  the  channel ; 
column  (c)  is  a  closed  section  and  is  seldom  used  on  that  account.  The 
cost  of  the  shop  work  on  column  (b)  was  formerly  considerably  more 
than  for  column  (a),  for  the  reason  that  it  was  impossible  to  use  a 
power  riveter  for  driving  all  the  rivets.  A  pneumatic  riveter  is  now 
made,  however,  that  will  drive  all  the  rivets  in  column  (b),  and  the 
shop  cost  for  columns  (a)  and  (b)  are  practically  the  same. 

Where  very  heavy  loads  are  to  be  carried,  columns  (d)  or  (e)  are 
often  used.  Column  (d),  composed  of  two  channels  and  one  I  beam, 
is  a  very  economical  column  and  is  quite  often  used  as  a  substitute  for 
the  Z-bar  column  shown  in  (e),  for  the  reason  that  it  can  be  built  up 
out  of  the  material  that  is  in  stock  or  that  can  be  easily  obtained.  Con- 
nections for  beams  are  easily  and  effectively  made  with  either  columns 
(d)  or  (e).  The  special  I  beam  column  (j),  with  flanges  equal  to  the 
depth  of  the  beam,  is  now  being  rolled  in  Germany  by  the  use  of  a 
process  patented  by  an  American,  Mr.  Henry  Grey.  This  column  makes 
an  almost  ideal  column  for  heavy  loads,  since  it  has  all  the  advantages 
of  the  Z-bar  column  with  a  very  much  smaller  shop  cost.  The  Larimer 
column  (k)  is  a  patented  column  manufactured  by  Jones  &  Laughlins, 
and  is  used  by  their  patrons  quite  extensively.  The  Gray  column  (1) 
is  a  patented  column  and  is  but  little  used.  Columns  made  of  four 
angles  box-laced,  are  used  where  extremely  light  loads  are  carried  by 
very  long  columns.  The  shop  cost  of  column  (m)  is  somewhat  less 
than  that  of  column  (n),  although  with  small  angles  there  is  no  dif- 
ficulty in  riveting  (n)  with  a  machine  riveter.  Column  (o)  is  a  very 
poorly  designed  column,  for  the  reason  that  the  radius  of  gyration  is 
very  small  for  the  area  of  a  cross-section  of  the  column.  Columns 
made  of  two  angles  "starred"  and  fastened  at  intervals  of  two  or  three 


COLUMN  DETAILS  205 

feet  by  means  of  batten  plates,  are  quite  frequently  used  for  light  loads. 
Column  Details. — The  details  of  a  4-angle  laced  column  attached 
to  a  truss  are  shown  in  Fig.  96 ;  and  the  details  of  a  4-angle  plate  column 
are  shown  in  Fig.  97.  The  details  of  bases  for  4-angle,  I  beam  and 
angle  columns  are  shown  in  Fig.  99. 


10) 


(O 


Shop  details  of  a  4-angle  column  are  shown  in  Fig.  100.  This 
column  was  designed  for  a  mill  building  with  a  span  of  60  feet,  trusses 
spaced  16  feet  apart.  The  long  legs  of  the  angles  are  placed  out,  to  give 
a  larger  radius  of  gyration  about  an  axis  at  right  angles  to  the  direc- 
tion of  the  wind.  The  details  of  a  4-angle  and  plate  column,  designed 
to  carry  a  crane  girder  as  well  as  the  roof,  are  shown  in  Fig.  101. 

The  details  of  a  heavy  column  composed  of  two  channels  placed 
back  to  back  and  laced,  are  shown  in  Fig.  102 ;  the  lacing  is  heavy  and 
is  well  riveted.  The  bent  plate  connections  for  the  anchor  bolts  on 
this  column  are  very  satisfactory.  This  is  one  of  the  columns  used  in 
the  A.  T.  &  S.  F.  R.  R.  shops  at  Topeka,  Kas.,  to  carry  the  crane 
girders. 

The  shop  details  of  a  light  channel  column  are  shown  in  Fig.  103. 
The  single  lacing  alternates  on  the  two  sides  of  the  column.  The 
various  details  of  the  columns  can  be  seen,  and  require  no  explanation. 


206 


FRAMEWORK 


Center  Roof  Truss. 


t;i~H 


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Q_         ^  ^<V|l\4l\jA4 


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l^'HoMx 


1-Pl.l&"*3%.''*2'9'4' 

z-e'xe'VjZ  £ 

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IHI  ENOINEERINO  RECORC 


FIG.  100. 


FIG.  101. 


COLUMN  DETAILS 


207 


I f=l,  il'-l- 

• 


N     *tf*r*fo- 


ft* 


x!-*- 


*t' 


:-S  / 


FIG.  102. 


FIG.  103. 


208 


FRAMEWORK 


Mam  Column  irt  Bending  and  Forge  Shop. 


Main  Side  Column  in  Bending  and  Forge  Shop 


FIG.  io3a.  FIG.  103!}. 

Details  of  columns  designed  to  carry  crane  girders  are  shown  in 
Figs.  iO3a,  iO3b,  IO3C,  and  iO3d,  which  have  been  taken  from  the 
Engineering  Record. 


COLUMN  DETAILS 


209 


Center  'Column    irt  Machino  Shop. 


FIG.  1030. 


<n  Column  No  J8.  ft«t>«««« 
orth  and  So«Xh  A*w* 

FIG.  I03d. 


210 


FRAMEWORK 


The  American  Bridge  Company's  specifications  for  lattice  bars  for 
single  and  double  lacing  are  shown  in  Fig.  104. 


Maximum  Distance  C  for  giren  thickness  of  bar. 


SINGLE  I 

JkCfNG  t  -  £) 

DOUBLE   I.ACI 

^t-% 

THICK. 
1 

DISTANCE 
C 

DISTANCE 
C 

THICK. 
t 

£ 

0-10 

1-    3 

i 

tj 

1       Oi 

1-    6* 

I 

-f 

1       3 

1-1CH 

t 

a 

1       5* 

2  -    2* 

fe 

ft 

1       8 

2-    6 

i 

I 

1     10* 

2  -    9J- 

I 

1 

2-    1 

3-    li 

1 

I  Rivet  I  Rivet 

*    r  ^         ^TJ= 

(Cj>        •*$  (0     -ri.j 

M—-  -*+  M -'-•*- 

UJ  t.*j 


O  *m 


CD- 


FIG.  104. 


UftJ 


Single  lacing  should  make  an  angle  of  not  less  than  60  degrees, 
and  double  lacing,  riveted  at  the  center,  not  less  than  45  degrees  with 
the  axis  of  the  member.  These  specifications  are  standard. 

The  properties  of  angles,  I  beams  and  channels,  and  of  Z-bar, 
Larimer  and  Gray  columns  are  given  in  the  manufacturers  handbooks. 
The  moment  of  inertia  of  two  channels  placed  back  to  back  and  laced, 
as  in  (a)  or  (b)  Fig.  98,  about  an  axis  parallel  to  the  webs  and  through 
the  center  of  gravity  of  the  section,  is  given  by  the  formula 

I  =  2  T  +  2  Ad2 

where  /'  =  moment  of  inertia  of  one  channel  about  an  axis  through 
its  center  of  gravity  and  parallel  to  the  given  axis,  A  =  the  area  of  one 
channel,  and  d  =  distance  from  the  center  of  gravity  of  one  channel 
to  the  center  of  gravity  of  the  column.  The  lacing  is  omitted  in  find- 
ing the  moment  of  inertia  and  the  area  of  the  section.  The  moment  of 
inertia  of  the  column  about  an  axis  perpendicular  to  the  webs  is  equal 


STRUTS  AND  BRACING  2 1 1 

to  twice  the  moment  of  inertia  of  one  channel,  which  may  be  found  in 
the  table  of  properties  of  channels  given  in  the  handbooks. 

Having  the  moment  of  inertia  7,  the  radius  of  gyration  of  the 
column  is  given  by  the  formula 


With  channels  placed  back  to  back  and  laced,  the  radii  of  gyra- 
tion about  the  two  axes  are  equal  when  the  clear  distance  is  equal  to 
about  3  inches  for  5-in.  channels,  and  10  inches  for  15-in.  channels.  A 
common  rule  is  to  space  the  channels  about  eight-tenths  the  depth. 
\Yith  channels  placed  with  backs  out  and  laced,  the  radii  of  gyration 
about  the  two  axes  are  equal  when  the  clear  distance  is  about  equal  to 
5  inches  for  5-in.  channels,  and  13  inches  for  15-in.  channels  (see 
Cambria  Steel,  1903  Edition,  p.  217). 

The  moment  of  inertia  of  a  4-angle  laced  column,  about  an  axis 
perpendicular  to  the  lacing  and  through  the  center  of  the  post,  is  given 
by  the  formula 

7  =  4/'  +  4Ad2 

where  I'  =  moment  of  inertia  of  one  angle  about  an  axis  through  its  cen- 
ter of  gravity  and  parallel  to  the  given  axis,  A  •==  the  area  of  one  angle 
and  d  =  the  distance  from  the  center  of  gravity  of  the  separate  angles 
to  the  center  of  gravity  of  the  column.  The  moment  of  inertia  about 
the  other  axis  is  found  in  a  similar  manner. 

STRUTS  AND  BRACING.— Eave  struts  are  very  commonly 
made  of  four  angles  laced,  made  in  the  same  way  as  the  4-angle  posts, 
Fig.  100.  Eave  struts  made  of  single  channels  are  more  economical, 
and  are  equally  as  good  as  the  laced  struts  for  most  cases.  End  rafters 
are  commonly  made  of  channels.  The  sides,  ends,  upper  and  lower 
chords  are  commonly  braced  as  shown  in  Fig.  81.  The  bracing  in  the 
plane  of  the  lower  chords  should  preferably  be  made  of  members  cap- 
able of  taking  compression  as  well  as  tension.  The  diagonal  bracing 
in  the  plane  of  sides,  ends,  and  upper  chords  is  commonly  composed  of 
rods.  Initial  tension  should  always  be  thrown  into  diagonal  rods  by 


212 


FRAMEWORK 


screwing  up  the  turnbuckles  or  adjustable  ends.  Stiff  bracing  should 
be  made  short,  and  should  be  brought  into  position  for  riveting  by  using 
drift  pins ;  to  accomplish  this  there  should  be  not  less  than  three  rivet 
holes  in  each  lateral  connection.  A  connection  for  lateral  rods  to  the 
chords  of  trusses  is  shown  in  Fig.  105. 


Lateral  Connection 
FIG.  105. 

Cast  lateral  lugs  for  connecting  lateral  rods  to  the  webs  of  I 
beams  and  to  heavy  plates  are  shown  in  (a)  and  (b),  Fig.  1 06. 


(2) 


N-~  If -<*--!  I* -MM 


Cast  Lateral  Lug 
(a) 


Cast  Lateral  Lug 

(b) 
FIG.  106. 

Where  rod  bracing  in  the  ends  and  sides  of  buildings  interferes 
with  windows  and  doors,  or  where  the  building  is  to  be  left  open,  portal 
bracing  is  used.  In  the  latter  case  the  bents  are  usually  braced  in  pairs, 


DESIGN  OF  PARTS  OF  THE  STRUCTURE;  213 

although  the  portal  bracing  is  sometimes  made  continuous.  Stiff  brac- 
ing is  often  placed  between  the  trusses  in  the  plane  of  the  center  of 
the  building  and  materially  stiffens  the  structure  (see  Fig.  175)". 

PURLINS  AND  GIRTS.— Purlins  are  made  of  channels,  angles, 
Z-bars  and  I  beams,  Fig.  in,  where  simple  shapes  are  used.  Channel 
and  angle  purlins  should  be  fastened  by  means  of  angle  lugs  as  shown 
in  Fig.  107.  I  beam  purlins  are  very  often  fastened  as  shown  in  the 
A.  T.  &  S.  F.  R.  R.  shops,  Fig.  175.  Z-bar  purlins  are  bolted  direct- 
ly to  the  upper  chords  of  the  trusses.  The  channel  purlin  is  the  most 
economical,  and  the  I  beam  purlin  is  the  most  rigid.  Girts  are  made 
of  channels,  angles,  and  Z-bars,  and  are  fastened  as  shown  in  Fig.  HI. 
Where  the  distance  between  trusses  is  more  than  15  or  16  feet  the  pur- 
lins and  girts  should  be  kept  from  sagging  by  running  ^  or  ^2 -inch 
rods  through  the  centers  to  act  as  sag  rods,  the  ends  of  the  rods  being 
fastened  to  the  eaves  and  ridge  (see  Fig.  81). 


-Purlin 


Purlin  Clip 
FIG.  107. 

Where  the  columns  and  trusses  are  placed  so  far  apart  that  the 
use  of  simple  rolled  shapes  is  no  longer  economical,  purlins  and  girts  are 
trussed. 

DESIGN  OF  PARTS  OF  THE  STRUCTURE.— The  methods 
of  determining  the  sizes  of  the  various  members  in  a  mill  building  will 
be  illustrated  by  a  few  examples.  For  a  more  detailed  treatment  of  this 
subject,  see  "Modern  Framed  Structures"  by  Johnson,  Bryan  and 
Turneaure ;  "Roofs  and  Bridges"  by  Merriman  and  Jacoby ;  and  other 
standard  works  on  bridge  design. 

Manufacturers  of  structural  material  issue  handbooks  which  con- 


214  FRAMEWORK 

tain  tables  that  give  weights,  areas  of  sections,  positions  of  centers  of 
gravity,  moments  of  inertia,  radii  of  gyration,  etc.,  for  the  shapes 
manufactured  by  the  different  companies.  Tables  are  also  given  for 
the  resisting  moments  on  pins,  the  shearing  and  bearing  values  of  rivets, 
standard  bolts,  eye-bars,  bridge  pins,  standard  connection  angles,  bear- 
ing plates,  minimum  size  of  rivets,  spacing  of  rivets,  and  many  other 
useful  tables.  The  handbooks  best  known  are  as  follows,  the  popular 
name  being  given  in  brackets :  Cambria  Steel  (Cambria),  issued  by  the 
Cambria  Steel  Company,  Johnstown,  Pa.;  Pocket  Companion  (Car- 
negie), issued  by  the  Carnegie  Steel  Company,  Pittsburg,  Pa.;  Stand- 
ard Steel  Construction  (Jones  &  Laughlins),  issued  by  Jones  &  Laugh- 
hns,  Limited,  Pittsburg,  Pa.;  Steel  in  Construction  (Pencoyd),  issued 
by  A.  and  P.  Roberts  Company,  Philadelphia ;  and  Structural  Steel  and 
Iron  (Passaic),  issued  by  the  Passaic  Rolling  Mill  Company,  Pater- 
son,  N.  J.  These  books  can  be  obtained  for  from  50  cts.  to  $2.00.  The 
American  Bridge  Company  issued,  in  1901,  a  book  entitled  Standards  for 
Structural  Details,  for  use  at  its  various  plants. 

The  Carnegie  handbook  was  formerly  very  generally  used  in  de- 
signing offices,  but  recently  the  supply  has  been  limited  so  that  the  Cam- 
bria handbook  has  taken  its  place  in  schools  and  in  many  offices,  and 
for  this  reason  references  will  be  made  to  Cambria  in  obtaining  weights, 
properties  of  sections,  etc.  All  references  to  Cambria  will  be  to  the 
1903  edition. 

Design  of  Trusses. — The  method  of  determining  the  proper  sizes 
of  the  truss  members  will  be  illustrated  by  designing  a  few  of  the 
members  of  the  truss  in  the  transverse  bent  of  the  mill  building  shown 
in  Fig.  53 ;  the  stresses  in  which  are  given  in  Table  VI.  The  secondary 
members  will  be  omitted  from  the  truss  in  the  design,  as  they  were  in 
obtaining  the  stresses. 

The  material  will  be  assumed  to  be  medium  steel  and  the  allow- 
able stresses  as  given  in  Appendix  I,  will  be  taken.  The  allowable 
stresses  are  as  follows: 

Tension 16,000  Ibs.  per  sq.  in. 

Compression 16,000  —  70  /  -j-  r  Ibs.  per  sq.  in. 


DESIGN  OF  TRUSSES  215 

where  /  =  the  length  of  the  member  in  inches,  and  r  —  radius  of  gyra- 
tion of  member  in  inches. 

Rivets  and  Pins,  bearing 22,000  Ibs.  per  sq.  in. 

Rivets  and  Pins,  shear 11,000     "     "     "     " 

Pins,  bending  on  extreme  fibre 24,000     "     "     "     " 

Plate  Girder  webs,  shear  on  net  section 10,000     "     "     "     " 

Compression  Members. 

Piece  x-2.  Maximum  stress  =  +  34,300  Ibs. 

The  upper  chord  will  be  made  of  two  angles  with  unequal  legs 
placed  back  to  back,  with  the  shorter  legs  turned  out,  and  separated  by 
^-inch  gusset  or  connection  plates. 

Try  two  4"  x  3"  x  5-16"  angles.  From  table  on  page  187  Cambria, 
the  least  radius  of  gyration,  r,  is  1.27  inches.  The  unsupported  length 
of  the  member  is  8.5  feet,  and  /-=-r  =  102  -f- 1.27  =  80.  The  allow- 
able stress  per  square  inch  =  16,000  —  70  /  -~-  r  =  16,000  —  5,600  = 
10,400  Ibs.  The  area  required  will  be  34,300  -f-  10,400  =  3.3  sq.  in. 
The  combined  area  of  the  two  angles  is  4.18  sq.  ins.  (page  170  Cam- 
bria), which  is  somewhat  large. 

Try  two  3*^"  x  3"  x  5-16"  angles.  From  the  table  on  page  186 
Cambria,  r  =  1 . 10  inches ;  then  /  -f-  r  =  93,  and  allowable  stress  is 
16,000  —  70  x  93  =1  9,490  Ibs.  per  sq.  in.  Required  area  =  3.62  sq.  in. 
The  area  of  the  two  angles  is  3.88  sq.  in.,  so  the  section  is  sufficient. 

To  make  the  two  angles  act  together  as  one  piece  it  is  necessary  to 
rivet  them  together  at  intervals,  such  that  the  two  angles  acting  singly 
will  be  stronger  than  the  two  angles  acting  together.  On  page  170 
Cambria,  the  least  radius  of  gyration  of  a  3^/2"  x  3"  x  5-16"  angle  about 
a  diagonal  axis  is  0.63  inches.  The  angles  must  therefore  be  riveted 
at  least  every  0.63  x  93  =  58.6  inches.  It  is  the  common  practice  to 
rivet  angles  in  compression  about  every  2^2  to  3  feet. 

The  truss  will  be  shipped  in  two  parts  and  in  order  to  avoid  a 
splice,  and  because  the  difference  in  the  stresses  is  small,  the  entire  top 
chord  will  be  made  of  two  3j^"  x  3"  x  5-16"  angles. 


216  FRAMEWORK 

Tension  Members. 

Member  1-2.  Maximum  stress  =  —  24,900  Ibs. 

The  net  area  required  is  24,900  -=-  16,000  =  1.56  sq.  in.  The 
gross  area  of  the  section  must  be  such,  that  there  will  be  a  net  area  of 
not  less  than  i .  56  sq.  in.  after  the  area  of  the  rivet  holes  in  any  section 
has  been  deducted. 

Try  two  3"  x  3"  x  J4"  angles.  It  will  be  necessary  to  deduct  the 
area  of  one  rivet  hole  from  each  angle.  The  diameter  of  the  rivet  hole 
deducted  is  taken  %  inch  larger  than  the  diameter  of -the  rivet  before 
driving.  Assuming  the  rivets  as  ^  inch,  it  will  be  necessary  to  deduct 
o.  19  sq.  in.  from  each  angle  (page  310  Cambria).  The  net  area  of  two 
3"  x  3"  x  y\"  angles  is  2.88  —  0.38  =  2.50  sq.  in.  The  section  is 
somewhat  large,  but  will  be  used,  for  the  reason  that  angles  much 
smaller  than  these  will  be  deficient  in  rigidity. 

The  angles  will  be  riveted  together  about  every  3  feet  to  make  them 
act  as  one  member. 

Member  5-6.  Maximum  stress  =  —  5,ooo  Ibs. 

The  net  area  required  is  5,000  -=-  16,000  =  0.32  sq.  in.  The  gross 
area  of  the  section  must  be  such  that  there  will  be  a  net  area  of  at  least 
0.32  sq.  in.  after  the  area  of  the  rivet  holes  in  any  section  has  been 
deducted. 

Try  two  2"  x  2"  x  y^"  angles  —  the  minimum  angles  that  can  be 
used  under  the  specifications.  Deducting  the  area  of  one  rivet  the  net 
area  is  1.88  —  0.38  =  1.50  sq.  in.  The  section  appears  to  be  exces- 
sively large  and  one  2"  x  2"  x  y^"  angle  will  be  tried.  Where  angles 
in  tension  are  fastened  by  one  leg  the  specifications  require  that  (para- 
graph 35)  only  one  leg  shall  be  counted  as  effective,  or  the  eccentric  stress 
shall  be  calculated.  The  net  area  of  the  one  2"  x  2"  x  %  "  angle  when 
fastened  by  one  leg,  will  then  be  J/£  0.94  —  o.  19  =  0.28  sq.  ins.,  which 
is  insufficient.  One  2^"  x  2^"  x  J4"  angle  will  have  a  net  area  of  0.40 
sq.  in.,  which  will  be  sufficient.  However,  since  it  is  preferable  to  make 
tension  members  of  symmetrical  sections,  the  member  will  be  made 
of  two  2"  x  2"  x  */4"  angles. 


DESIGN  OF  COLUMNS  217 

Alternate  Tension  and  Compression.-^Where  members  are  subject 
to  alternate  tension  and  compression  the  specifications  require  that  they 
be  designed  to  take  each  kind  of  stress,  (paragraph  32). 

Member  4-y.  Maximum  stresses  =  ( — 2 1,300  and  +  2600  Ibs). 

Try  two  3"  x  3"  x  %"  angles  —  the  same  as  member  1-2.  The 
net  area  required  for  tension  is  21,300  -=-  16,000  =  1 .34  sq.  in. 

The  net  area  of  two  3"  x  3"  x  J4"  angles  is  2.88  —  0.38  =  2.50 
sq.  in.  which  is  ample  for  tension. 

The  least  radius  of  gyration  is  r  =  0.93  inches  (page  185  Cam- 
bria). Length  =  108  inches,  and  /  -r-  r  =  117.  The  allowable  stress 
per  square  inch  =  16,000  —  70  x  117  =  8,810  Ibs.  Required  area  = 
0.30  sq.  in.  The  section  appears  to  be  large,  but  it  can  not  be  made 
much  smaller  without  exceeding  the  maximum  limit  of  125  for  /  -f-  r. 
Two  3"  x  2^"  x  *4"  angles  will  be  found  by  a  similar  calculation  to  be 
sufficiently  large,  and  will  be  used. 

Member  3-4.  Maximum  stresses  =  ( —  10,900  and  -|*  13,600  Ibs). 

Try  two  2"  x  2"  x  y±"  angles.  The  area  required  to  take  the  ten- 
sion is  10,900  -f-  16,000  =  0.69  sq.  in.  The  net  area  of  the  two 
angles  is  1 .88  —  0.38  =  1 .50  sq  in.,  which  is  ample  for  tension.  The 
least  radius  of  gyration  is  r  •=  0.61  inches  (page  185  Cambria).  The 
length  is  108  inches,  and  l-z-r  =  177.  This  is  greater  than  the  max- 
imum allowed  of  125,  and  a  larger  section  must  be  used. 

Try  two  3"  x  2"  x  y±"  angles,  with  short  legs  out.  In  this  case 
I  -=-  r  equals  108  -j-  0.89  =  120.  The  allowable  stress  per  sq.  in.  is 
16,000  —  70  x  120  =  7,600  Ibs.  The  required  area  for  compression  is 
13,000  -i-  7,600  =1.79  sq.  in.  The  area  of  the  two  angles  is  2.38  sq. 
in.,  which  is  ample.  The  section  is  sufficiently  large  to  take  both  ten- 
sion and  compression,  and  will  be  used. 

Design  of  Columns. — Columns  must  be  designed  to  take  the 
stress  due  to  direct  loading,  to  eccentric  loading,  and  to  wind  moment. 
The  method  of  column  design  will  be  illustrated  by  the  design  of  the 
leeward  column  in  the  transverse  bent  shown  in  Fig.  56 ;  the  stresses  for 
which  are  given  in  Table  VI. 


2i  8  FRAMEWORK 

Direct  stress  in  A-iJ  =    14,900  Ibs. ;  and  bending  moment  = 
924,000  inch-lbs.    A  4-angle  laced  column  will  be  used. 

Try  four  4"  x  3"  x  5-16"  angles,  long  legs  out,  and  a  depth  of 
18"  out  to  out  of  angles ;  y%'  lacing  and  connection  plates  will  be  used. 
The  radius  of  gyration  of  two  4"  x  3"  x  5-16"  angles  with  the  long 
legs  out,  is  found  on  page  189  Cambria  to  be  1.93  inches. 

The  moment  of  inertia  of  a  section  of  the  post  about  the  shorter 
axis  is 

7  =  4  /'  +  4  Ad2 

=  4  x  1.65  +  4  x  2.09  (9.00  —  0.76)* 
=  574.24 
and  the  radius  of  gyration  is 

574.24 


8. 3  inches. 

The  maximum  fibre  stress  will  occur  on  the  windward  side  of  the 
post  and  will  be  found  by  substituting  in  formula  (3oa)  to  be 

14,900       924,000  X  9 

7  — /3+/i=      g>36      1-  14, 900  X  24Q2 

•2          280,000,000 

=  1780  +  14,560  =  16,340  Ibs.  per  square  inch. 
The  allowable  stress  per  square  inch  for  direct  loads  is  16,000  — 
70  /  -r-  r  =  16,000  —  70  x  29  =  14,000  Ibs. ;  and  since  the  wind  mo- 
ment comes  only  occasionally  we  will  increase  the  allowable  stress  for 
direct  loads  by  25  per  cent  when  wind  loads  are  considered,  making  an 
allowable  stress  of  14,000  x  1.25  =  17,500  Ibs.  per  square  inch.  The 
section  chosen  is  therefore  sufficiently  large. 

The  direct  load  will  have  to  be  carried  by  the  column,  and  it  will 
be  necessary  to  investigate  the  column  about  its  longer  axis.  For  this 
case  /  -r-  r  =  240  -r-  1 .93  =  125,  which  is  allowable  under  the  specifica- 
tions, and  the  section  is  ample. 

The  lacing  will  be  designed  to  take  the  shear,  which  is  5,500  Ibs. 
below  and  12,800  Ibs.  above  the  foot  of  the  knee  brace.  The  maximum 
stress  in  the  lacing  will  be  12,800  x  sec  30°  =  14,700  Ibs.  The  al- 
lowable tensile  stress  per  square  inch  will  be  16,000  x  i .  25  =  20,000 


TABLES 


219 


TABLE  XI. 

SPACING  IN  ANGLES. 


G 

c=^ 

iffL 

F 

Leg. 

Inches. 

Inches. 

Max. 
Rivets. 
Inches. 

Leg. 
Inches. 

Inches. 

Inches. 

Max. 
Rivets. 
Inches. 

8 
7 
6 
5 
4 

3  2 

t 

M 
M 
M 

8 
7 
6 
5 

3 

3 
3 

1M 

X 

"Where  6"  Angle  Exceeds  %". 

6 

** 

« 

% 

TABLE  XII. 
MAXIMUM  SIZE  OF  RIVETS  IN  BEAMS,  CHANNELS,  AND  ANGLES. 


I-BEAMS. 

CHANNELS. 

ANQLES. 

Depth 

Wsiglrt 

Size 

Dipth 

Weight 

Size 

Depth 

Weight 

Size 

Length 

Size 

Length 

Size 

of 

per 

or 

01 

per 

of 

of 

per 

of 

of 

of 

of 

of 

3e»E. 

Foot. 

Rivet. 

Be»m. 

Foot. 

Rivet. 

Chinnel 

Foot. 

Rivet. 

Leg. 

Rivet. 

Leg. 

Rivet. 

Injk's. 

Pounds. 

Inches. 

Inches. 

Pounds. 

Inshes. 

lushes. 

Pounds. 

Inches. 

Inshes. 

Inches. 

Inches. 

Inches. 

3 

5.5 

% 

15 

42.0 

X 

3 

4.0 

H 

y, 

H 

2K 

M 

4 

7.5 

% 

15 

60.0 

X 

4 

5.25 

# 

# 

2# 

* 

5 

9.75 

*/2 

35 

80.0 

# 

5 

6.5 

>/2 

IX 

/2 

3 

6 

12.25 

# 

18 

55.0 

# 

6 

8.0 

# 

IA 

/2 

3X 

1 

7 

15.0 

% 

20 

65.0 

7 

9.75 

% 

1H 

>/2 

4 

1 

8 

18.0 

X 

20 

80.0 

1 

8 

11.25 

X 

1/2 

*/* 

4K 

1 

9 

21.0 

y* 

24 

80.0 

1 

Q 

13.25 

X 

1^ 

H 

5 

1 

10 

25.0 

% 

10 

15.0 

y. 

2 

tt 

6 

1 

12 

31.5 

y* 

12 

20.50 

y, 

2^ 

y 

7 

1 

12 

40.0 

y< 

15 

33.0 

y 

2A 

y 

16 


220 


FRAMEWORK 


TABLE  XIII. 
RIVET  SPACING. 


Sixe 
of 

Bivet. 

Inches. 

Minimum 
Pitch. 

Inches. 

Maximum  Pitch  at 
Ends  of 
Compression 
Members. 
Inches. 

Minimum  Pitch  in 
Flanges  of 
Chords  and  Sird's. 

Inches. 

Distance  from  Edge  of  Piece  to 
Center  of  Rivet  Hole. 

Minimum. 
Inches. 

Usual. 
Inches. 

I 

1 

3  * 

V" 

4 

"it 

'i* 

1 

3 

4 

4 

4 

11 

2 

TABLE  XIV. 
SHEARING  AND  BEARING  VALUE  OF  RIVETS  IN  POUNDS. 


Diameter  of 
Rivet 
Inches 

Area 
in 
Square 
Inches. 

Single 
Shear 
at  11000 
Lbs. 

Bearing  Value  for  Different  Thicknesses  of  Plate   in 
Inches,  at  22,000  Pounds  per  Square  Inch. 

X 

.I. 
ie 

* 

JL 

16 

% 

s. 
ie 

H 

11 

16 

u 

Frac- 
tion 

Deci- 
mal 

* 

*6 

a 

%' 
y* 
i 

.375 
.500 
.625 
.750 
.875 
1.00 

.1104 
.1963 
.3068 
.4'418 
.6013 
.7854 

1210 
2160 
3370 
4860 
6610 
8640 

2060 
2750 
3440 

2580 

3090 

4820 
6020 
7220 
8430 
9630 

5500 

6880 

7740 

8600 
10320 

•aanBBBi^ 

12040 
13750 

11340 
13240 

12380 

14440 

3440 
4300 
5160 

m^mum^i 

6020 
6880 

4130 
5160 
6190 

7220 

4130 
4810 
5500 

8250 
9630 
11000 

9280 
10840 
12380 

8250 

15130 

16500 

All  bearing  values  above  or  to  right  of  upper  zizgag  lines  are  greater  than  double  shear. 
Values  below  or  to  left  of  louver  zigzag  lines  are  less  than  single  shear. 

Ibs.  The  required  net  area  for  tension  will  be  14,700  -.-  20,000  =  0.74 
square  inches.  The  gross  area  of  a  3"  x  y%"  bar  is  1 . 125  square  inches 
(page  388  Cambria)  and  the  net  area  after  deducting  for  one  ^4"  rivet 
is  0.795  square  inches  (page  310  Cambria)  which  is  sufficient  for 
tension. 


DESIGN  OF  PLATE  GIRDERS  221 

The  allowable  stress  for  compression  is  (16,000  —  7O/-r-r)  1.25. 
The  moment  of  inertia  of  a  3"  x  ^g"  bar  is  0.0135,  and  the  radius  of 
gyration  is  o.n  inches.  The  ends  of  the  lacing  bars  are  practically 
fixed,  and  it  will  be  assumed  that  the  length  c.  to  c.  of  rivets  will 
as  a  result  be  shortened  by  one-half.  Then  l-s-r  =  75,  the  allowable  stress 
will  be  13,340  Ibs.  and  the  required  area  1 . 10  square  inches.  The  lao 
ing  bars  are  therefore  sufficient  to  take  either  the  tension  or  compression. 
Lacing  bars  2^2"  x  y%'  will  be  found  sufficient  below  the  foot  of  the 
knee  brace. 

The  allowable  shear  on  each  rivet  in  the  lacing  will  be  (Table  XIV) 
4860  x  1.25  =  6,075  Ibs.;  and  the  allowable  bearing  will  be  6,190  x 
1.25  =  7,740  Ibs.  The  stress  in  the  lacing  bars  below  the  foot  of  the 
knee  brace  is  5,500  x  sec  30°  =  6,300  Ibs. ;  the  24 -rivets  are  all  right 
for  bearing  but  are  not  quite  large  enough  for  shear,  however  it  is  so 
near,  that  they  will  be  used.  Above  the  foot  of  the  knee  brace  it  will  be 
necessary  to  increase  the  thickness  of  the  lacing  bars  and  put  two  rivets 
in  each  connection  as  shown  in  Fig.  102,  or  use  a  solid  plate. 

In  designing  the  bases  of  columns  hinged  at  the  base,  part  of  the 
stresses  may  be  assumed  to  pass  directly  to  the  base  plate  if  the  abutting 
surfaces  have  been  milled;  but  in  columns  fixed  at  the  base  all  of  the 
stresses  must  be  transferred  by  the  rivets.  The  rivets  must  be  designed 
to  take  the  direct  stress  and  the  stress  due  to  bending  moment ;  the  so- 
lution is  similar  to  that  for  anchorage  (Fig.  61)  and  will  not  be  given. 

Design  of  Plate  Girders. — The  maximum  moments  and  shears 
are  found  as  described  in  Chapter  X.  If  the  plate  girder  were  de- 
signed by  means  of  its  moment  of  inertia,  as  in  the  case  of  rolled  sec- 
tions, about  %  of  the  web  would  be  effective  as  flange  area  to  take 
the  bending  moment ;  or  deducting  rivets  about  ^  would  be  found  ef- 
fective. It  is,  however,  the  common  practice  to  assume  that  all  the 
moment  is  taken  by  the  flanges,  and  that  all  the  shear  is  taken  by  the 
web ;  and  this  assumption  will  be  made  in  the  discussion  which  follows. 

Flange  Stress. — The  stress,  F,  in  the  flanges  at  any  point  in  a 
plate  girder  is 

F  =  M  -T-  h  (80) 


222 


FRAMEWORK 


where  M  =  bending  moment  in  inch-pounds,  and  h  =  the  distance 
between  centers  of  gravity  of  the  flange  areas  (effective  depth),  (a) 

Fig.  108. 

The  net  flange  area,  A,  will  be  A  =  P  -r-  f  where  /  =  the  allow- 
able unit  stress.  The  tension  flanges  of  plate  girders  are  designed  as 
above,  and  the  compression  flanges  are  made  with  the  same  gross  area. 


Neutral  Axis  — 


1>        -4 

n 

L-0-         0 

+P+ 

* 

: 

i>      i 

g 

g    ° 

r~  Flan  qe  A  ngles 


o     o     o 

o     o     o     o 

0       0 

3        0       O 

0  /£ 

^vs 

3     *"• 

0         -K 

J 

5          2 

o      | 

Web  Plate 

^ 

;  | 

^ 

| 

\  4 

o     o 

0000 

0      O 

3       0       O     \ 

f 

^Flange  Angles 
(b) 


•^^  i*-  Xj; 


O         < 

}     -( 

>-> 

r-0-           0 

.,. 

f 

0         ( 

S>     -< 

. 

L-o-       o 

(d) 
FIG.  108. 


(e) 


. — The  web  plate  should  not  be  less  than  5-16  of  an  inch  in 
thickness  although  >^-inch  plates  may  be  used  if  provided  with  suf- 
ficient stiffeners.  The  shear  in  the  web  is  commonly  assumed  as  uni- 
formly distributed  over  the  entire  cross-section  of  the  plate. 

Stiffeners. — There  is  no  rational  method  for  the  design  of  stif- 
feners. If  they  are  placed  at  distances  apart  not  exceeding  the  depth 
of  the  girder,  nor  more  than  5  feet,  where  the  shearing  stress  is  greater 


DESIGN  OF  PLATE  GIRDERS  223 

than  given  by  the  formula  —  allowed  shearing  stress  —  12,500  —  90  H, 
where  H  =  ratio  of  depth  to  thickness  of  web  plate,  the  stiffeners  will 
be  near  enough  together.  Where  the  shearing  stress  is  less  than  given 
by  the  above  formula,  stiffeners  may  be  omitted  or  spaced  as  desired. 

Stiffeners  are  commonly  designed  as  columns,  free  to  move  in  a  di- 
rection at  right  angles  to  the  web,  with  an  allowed  stress  P  =  12,000  — 
55  /  -4-  r.  Stiffeners  should  be  provided  at  all  points  of  support  and  un- 
der all  concentrated  loads,  and  should  contain  enough  rivets  to  transfer 
the  vertical  shear. 

Web  Splice. — In  the  plain  web  splice  shown  in  Fig.  io8a,  the  rivets 
take  a  uniform  shear  equal  to  S  -f-  n,  where  S  is  total  shear,  and  n 
is  number  of  rivets  on  one  side  of  splice,  and  a  shear  due  to  the  shearing 
stress  not  being  applied  at  the  center  of  gravity  of  the  rivets.  This  is 
the  problem  of  the  eccentric  riveted  connection,  which  has  been  dis- 
cussed in  Chapter  XV. 

If  the  web  is  assumed  to  take  part  of  the  bending  moment  there 
will  be  an  additional  shear  due  to  bending  moment. 

Rivets  in  the  Flanges. — In  Fig.  108,  let  S  =  the  shear  in  the  girder 
at  the  given  section,  h'  =  distance  between  rivet  lines,  p  =  the  pitch  of 
the  rivets,  and  r  •=.  the  resistance  of  one  rivet  (r  is  usually  the  safe 
bearing  on  the  rivet  in  the  web) . 

Then  taking  moments  about  the  lower  right  hand  rivet,  we  have 

Sp  =  rh',  and  p  =  rh'  -f-  S  (81) 

Where  the  rivets  are  in  double  rows  as  shown  in  (d),  the  distance 
h'  is  taken  as  a  me'an  of  the  distances  for  the  two  lines. 

The  crane  loads  produce  an  additional  shear  in  the  rivets,  (e)  Fig. 
1 08,  which  will  now  be  investigated.  We  will  assume  that  the  rail  dis- 
tributes the  load  over  a  distance  of  25  inches ;  this  distance  will  be  less 
for  light  rails  and  more  for  heavy  rails.  The  maximum  vertical  shear 
on  one  rivet  will  be  Pp  -f-  25  =  0.04  Pp.  The  horizontal  stress  due  to 
bending  moment  is  r  —  Sp  -r-  h',  and  the  resultant  stress  from  the  two 
sources  will  be 


224 


FRAMEWORK 


r'  = 


and  solving  for  p 


-v 


(0.04 


(82) 


Crane  Girders. — The  maximum  moments  and  shears  in  crane  gir- 
ders are  found  as  explained  in  Chapter  X.  For  small  cranes  I  beam 
girders  are  commonly  used,  and  are  designed  by  the  use  of  their  mo- 
ments of  inertia.  Plate  girders  are  designed  as  previously  described. 
In  designing  both  rolled  and  plate  girders  care  must  be  used  to  proper- 
ly support  the  girder  laterally. 


FIG.  io8a. 


CHAPTER  XVIII. 


CORRUGATED  STEEL. 

Introduction. — Corrugated  steel  is  made  from  sheet  steel  of  stand- 
ard gages,  and  is  either  galvanized  at  the  mill  or  is  left  black.  The 
black  corrugated  steel  is  usually  painted  at  the  mill  and  is  always  paint- 
ed after  erection.  Paint  will  not  adhere  well  to  the  galvanized  steel 
until  after  it  has  weathered  unless  a  portion  of  the  coating  is  removed 
by  the  application  of  an  acid.  The  common  standard  for  the  gage  of 
sheet  steel  in  the  United  States  is  the  United  States  Standard  Gage, 
and  this  should  be  used  in  specifying  the  weight  and  thickness.  The 
thickness  and  weights  per  square  of  100  square  feet,  for  black  and  gal- 
vanized sheet  and  corrugated  steel  are  given  in  Table  XV.  The  weights 
of  the  corrugated  steel  given  in  the  table  are  for  standard  corrugations, 
approximately  2^2  inches  wide  and  ^  of  an  inch  deep.  If  black  sheet 
steel  is  painted,  add  about  2  Ibs.  per  square. 

TABLE  XV. 
WEIGHT  OF  FLAT,  AND  CORRUGATED  STEEL  SHEETS  WITH  2* 

CORRUGATIONS. 


Gage  No. 

Thickness 
in 
inches 

Weight     per     Sq 

uare    (  100  sq-ft-) 

Flat  Sheets 

Corrugated  Sheets 

Black 

Galvanized 

Black  Painted 

Galvanized 

16 

.0625 

250 

266 

275 

291 

18 

.0500 

200 

216 

220 

236 

20 

.0375 

150 

166 

165 

Id2 

22 

.0313 

125 

/4l 

13d 

154 

24 

.0250 

too 

//6 

1  1  f 

127 

26 

•0/88 

75 

31 

84 

99 

28 

•0/56 

63 

79 

69 

66 

Corrugated  steel  is  also  made  with  corrugations  5,  3  and 
inches  wide  approximately.     Corrugated  s.teel  with  corrugations 


226 

inches  wide  and  ^  of  an  inch  deep  is  frequently  used  for  lining  build- 
ings. Corrugated  steel  with  i^-inch  corrugations  weighs  about  4  per 
cent  more  than  steel  of  the  same  gage  with  2^-inch  corrugations.  Cor- 
rugated sheets  are  commonly  made  from  flat  bessemer  steel  sheets,  by 
rolling  one  corrugation  at  a  time.  Iron  and  open  hearth  steel  corrugated 
sheets  can  be  obtained,  but  are  very  hard  to  get  and  cost  extra. 

The  standard  sheets  of  corrugated  steel  with  2.^/2  -inch  corrugations, 
are  28  inches  wide  before,  and  26  inches  wide  after  corrugating,  and 
will  cover  a  width  of  24  inches  with  one  corrugation  side  lap,  and  ap- 
proximately 213^  inches  with  two  corrugations  side  lap,  (c)  and  (a) 
Fig.  109.  Special  corrugated  steel  can  usually  be  obtained  that  will 
cover  a  width  of  24  inches  with  il/2  corrugations  side  lap,  (b).  Cor- 
rugated steel  should  be  laid  with  6  inches  end  lap  on  the  roof  and  4 
inches  end  lap  on  the  sides  of  buildings. 

Corrugated  Roof  Steel 
5ide  Lap  2  Corrugations 

~  -"i*  -  Covers  £/i*  --- 

__  jjr  _ 

|-  -  2dt  "w/'tfe  before  c&rrugar/ng 
r~26"    »    afrer 

(a) 

Special  Cor-  Roof  Steel 
Side  Lap  \k  Corrugations 
—  Covers  24"-  >h  -  Covers  Z4-"  --- 


-30  "w/'tfe  before  corrug&f/ng 
/?/^"  "    afrer 
for  Roof  6" 
(b) 

Corrugated  Siding  Steel 
Side  Lap  I  Corrugation 
—  Covers  24"-^*-  Coders  24  "  ~-- 


\*£d  "w/ae  before  cerrugat/rtg 
^26"  "   affer          » 
End  Lap  for5/des  4  " 

(C) 
FIG.  109. 


FASTENING  CORRUGATED 


227 


Stock  lengths  of  corrugated  steel  sheets  can  be  obtained  from  5 
to  10  feet,  varying  by  one-half  foot.  Sheets  of  any  length  between  4 
and  10  feet  can  usually  be  obtained  directly  from  the  mill  without  extra 
charge.  Sheets  from  48  to  5  inches  long,  cost  from  i-io  to  y*  cents  per 
pound  extra.  Sheets  from  10  to  12  feet  long  are  very  hard  to  obtain 
and  cost  extra.  Sheets  cannot  be  obtained  longer  than  12  feet.  Stock 
lengths  of  sheets  should  be  used  whenever  possible  as  odd  lengths  often 
delay  the  filling  of  the  order.  Bevel  sheets  should  preferably  be  ordered 
in  multiple  lengths  and  should  be  cut  in  the  field.  Sheets  to  fit  around 
windows  and  doors  should  be  cut  in  the  field;  no  part  of  a  sheet  less 
than  ±  the  width  of  a  full  sheet  should  ever  be  used. 


SECTION  A-A 


FIG.  no. 

For  cutting  and  splitting  corrugated  sheets  in  the  field  the  rotary 
shear  shown  in  Fig.  no  is  invaluable.  It  will  make  square  or  bevel 
cuts,  or  will  split  sheets  without  denting  the  corrugations.  The  shear 
shown  in  Fig.  no  is  one  made  by  the  Gillette-Herzog  Mfg.  Co.,  Min- 
neapolis, Minn.,  and  was  used  by  the  author  in  the  erection  of  a  steel 
stamp  mill  in  Northern  Michigan,  while  in  the  employ  of  the  above 
named  company.  The  shear  is  not  on  the  market,  but  can  be  made  in 
any  ordinary  machine  shop  at  a  comparatively  small  cost. 

Fastening  Corrugated  Steel. — Where  spiking  strips  are  used,  the 
corrugated  steel  is  fastened  with  8d  barbed  roofing  nails  24  to  2.^/2 
inches  long,  spaced  6  to  8  inches  apart.  The  2.^/2 -inch  barbed  nails 
should  be  used  for  nailing  to  spiking  strips  and  to  sheathing  whenever 
possible.  For  weight  of  barbed  roofing  nails  see  Table  XVI. 


228 


CORRUGATED  STEEL 


TABLE  XVI. 
NUMBER  OF  BARBED  ROOFING  NAILS  IN  ONE  POUND. 


Size 

Length 
inches 

Gage 

No. 

No.  in 
one  Ib. 

Size 

Length 
inches 

Gage 

No. 

No.  in 
one  Ib. 

4d 

IX 

13 

339 

20d 

4 

6 

30 

6d 

2 

12 

205 

30d 

4# 

5 

23 

8d 

2^ 

10 

96 

40d 

5 

4 

17 

lOd 

9 

63 

50d 

5^ 

3 

13 

12d 

3X 

8 

52 

60d 

6 

•2. 

10 

16d 

3X 

7 

38 

The  common  methods  of  fastening  corrugated  steel  directly  to 
the  purlins  and  girts  are  shown  in  Fig.  1 1 1 .  Nailing  pieces  should  pref- 
erably be  used  where  anti-condensation  roofing,  Fig.  127,  is  used,  or 
where  the  sides  are  lined  with  corrugated  steel.  The  clinch  nail  is  prob- 


sf, 


^  #*\ 
Rivers  ancf  c//nch  na/b  go      f{0°  u*S 

irougfi  fop  of  corrvg&t/om    (    ^( 

—  — i«w  *      **?  x-r* 


Methods  of  Fastening 
Corrugated  Steel  to  PUrlins 


Table  of  Clinch  Nails 


L  Purl  in  leq 
Length 
No-  per  Ib. 

y 

32 

4" 
6" 
29 

5" 
7" 
23 

6" 
8" 

21 

7" 
9" 
18 

C  Purlin  leg 
Lenqrh 
No-  per  Ib. 

3" 
6" 
29 

4" 
7"or8' 
21 

5" 
9" 
18 

6" 
SO" 
16 

7' 
//" 
fr 

FIG.  in.     METHODS  OF  FASTENING  CORRUGATED  STEEL  TO  PURLINS 

AND  GIRTS. 

ably  the  most  satisfactory  fastening  for  the  usual  conditions.    The  side 
laps  are  fastened  together  by  means  of  copper  or  galvanized  iron  clos- 


WEIGHT  OF  COPPER  RIVETS 


229 


ing  rivets,  spaced  about  8  to  12  inches  apart  on  the  roof  and  about  2 
feet  apart  on  the  sides. 

Clinch  nails  are  made  of  %  inch  or  No.  10  soft  iron  wire  and  are 
clinched  around  the  purlin.  The  usual  sizes  and  weights  of  clinch  nails 
for  different  lengths  of  angle  and  channel  purlins  are  given  in  Fig.  in. 
Care  should  be  used  in  punching  the  holes  in  the  corrugated  steel  for 
clinch  nails  and  rivets  to  get  them  in  the  top  of  the  corrugations  and 
to  avoid  making  the  hole  unnecessarily  large.  Clinch  nails  are  spaced 
from  8  to  12  inches  apart.  Two  clinch  nails  are  usually  furnished  for 
each  lineal  foot  of  purlin  and  girt. 

Straps  are  made  of  No.  18  gage  steel,  24  inches  wide,  and  are 

TABLE  XVII. 
NUMBER  OF  COPPER  RIVETS  IN  ONE  POUND. 


Diam- 
eter 
Gage 
No. 

Length  of  Rivets  in  inches. 

B 

X 

A 

% 

JL. 

16 

H 

A 

% 

% 

% 

i 

1* 

IK 

1V4 

3 

70 

4 

78 

5 

85 

64 

60 

53 

48 

46 

44 

39 

36 

32 

6 

180 

105 

100 

96 

90 

74 

68 

61 

56 

54 

50 

46 

7 

368 

211 

180 

171 

160 

150 

140 

132 

110 

97 

91 

79 

72 

63 

8 

417 

266 

248 

227 

200 

172 

157 

147 

136 

116 

100 

93 

88 

71 

9 

600 

365 

336 

261 

248 

228 

220 

184 

169 

156 

133 

124 

113 

99 

10 

820 

411 

376 

336 

305 

257 

249 

223 

206 

180 

162 

11 

944 

416 

400 

360 

338 

320 

12 

1167 

545 

475 

400 

342 

325 

308 

292 

257 

221 

190 

13 

1442 

799 

640 

547 

502 

448 

400 

392 

316 

14 

1620 

1040 

995 

816 

784 

616 

550 

528 

15 

3512 

fastened  with  two  3-i6-inch  stove  bolts  ^  inches  long.  Straps  are 
spaced  8  to  12  inches  apart.  One  strap  and  two  bolts  are  usually  fur- 
nished for  each  lineal  foot  of  purlin  and  girt.  One  bundle  of  hoop 
steel  for  making  straps  contains  400  lineal  feet  and  weighs  50  Ibs. 

Clips  are  made  of  No.  16  gage  steel,  iy2"  x  2%",  and  are  fastened 
with  two  3- 1 6-inch  stove  bolts  y2  inches  long.  Clips  are  spaced  from 
8  to  12  inches  apart.  One  clip  and  two  bolts  are  usually  furnished  for 
each  lineal  foot  of  purlin  and  girt. 


23° 


CORRUGATED 


Copper  rivets  weighing  about  6  pounds  per  1000  rivets  have  com- 
monly been  used  for  closing  rivets  ;  but  galvanized  iron  rivets  made  of 
vei«y  soft  wire  and  weighing  about  7  pounds  per  1000  rivets  are  fully 
as  good,  and  cost  7  cents  per  pound  in  1903  as  compared  with  about 
25  cents  per  pound  for  copper  rivets.  The  weight  of  copper  rivets  is 
given  in  Table  XVII. 

Strength  of  Corrugated  Steel.  —  The  safe  load  per  square  foot  for 
corrugated  steel  supported  as  a  simple  beam,  for  sheets  with  2.^/2  -inch 
corrugations  and  of  various  gages  is  given  in  Fig.  112.  This  diagram 
is  based  on  Rankine's  formula 


_ 
15 


where  W  =  safe  load  in  Ibs.  ; 

S  =  working  stress  in  Ibs.  ; 
h  =  depth  of  the  corrugations  in  inches  ; 
b  =  width  of  the  sheet  in  inches; 
t  =  thickness  of  the  sheet  in  inches  ; 
/  =  clear  span  in  inches. 


FIG.  112.    SAFE  UNIFORM  LOAD  IN  POUNDS  FOR  CORRUGATED  STEEL 
DIFFERENT  SPANS  IN  FEET. 

A  summary  of  experiments  to  determine  the  strength  of  corrugated 
steel  made  by  the  author's  assistant,  Mr.  Ralph  H.  Gage,  is  given  in 


STRENGTH  OF  CORRUGATED  STEEL 


231 


Table  XVIII.  The  coefficient  C  in  column  8  depends  on  the  angle  that 
the  metal  makes  with  the  horizontal  axis  and  varies  as  follows:  angle 
of  30°,  C  =  0.278 ;  45°,  C  =  0.293 ;  60°,  C  =  0.312,  and  for  90°,  C  = 
0-393- 

TABLE  XVIII. 

SUMMARY  OF  EXPERIMENTS  TO  DETERMINE  THE  STRENGTH  OF  COR- 
RUGATED STEEL.* 


1 

2 

3 

4 

5 

6 

7 

8 

9 

1O 

Width 

Thick- 

Angle 

Tensile 

Gage's 

Actual 

Rankine's 

No. 

of 

Depth 

ness 

of 

Span 

Strength 

Formula 

Brkng 

Formula. 

Corru- 

h 

t 

Metal 

/ 

Ibs.  per 

M  =  CShbt 

Load 

M=^Shbt 

gations 

with 

sq.  in. 

W 

Ins. 

Ins. 

Ins. 

Axis 

Ins. 

Ibs. 

Ibs. 

>     Ibs. 

1 

2.50 

0.6025 

.0588 

39°  11' 

44.0 

58,000 

643 

630 

597 

2 

2.50 

0.612 

.0568  39°  10'    44.0 

58,000 

632 

630 

587 

3 

2.50 

0.625 

.066    39°  30'!  44.0 

58,000 

745 

720 

692 

4 

2.50 

0.606 

.0655|40°42' 

44.0 

58,000 

725 

700 

670 

5 

2.88 

0.650 

.036736°   0'    43.25 

67,000 

505 

500 

475 

6 

2.88 

0.650 

.036636°    0'    44.0 

67,000 

494 

490 

465 

7 

2.50 

0.630 

.036636°   0'    44.0 

50,000 

358 

350 

335 

8 

2.50 

0.61 

.036536°   0' 

44.0 

50,000 

344 

340 

324 

9 

1.25 

0.27 

.036536°   0' 

24.0 

50,000 

281 

300 

262 

10 

1.25 

0.27 

.036536°   0' 

24.0 

50,000 

281 

295 

262 

11 

1.25 

0.27 

.029336°   0' 

24.0 

50,000 

225 

200 

211 

12 

1.25 

0.27 

.029336°   0' 

24.0 

50,000 

225 

195 

211 

13 

1.00 

0.18 

.029136°   0' 

24.0 

50,000 

298 

310 

279 

14 

1.00 

0.18 

.029136°  0' 

24.0 

50,000 

298 

300 

279 

15 

1.00 

0.18 

.026 

36°   0' 

24.0 

50,000 

266 

280 

250 

16 

1.00 

0.18 

.026 

36°   0' 

24.0 

50,000 

266 

260 

250 

The  actual  breaking  load  agrees  in  most  cases  more  closely  with 
Gage's  formula  than  with  Rankine's,  although  the  latter  is  more  often 
on  the  safe  side. 

Purlins  are  commonly  spaced  for  a  safe  load  of  30  Ibs.  per  square 
foot  as  given  in  Fig.  112;  if  the  purlins  are  spaced  farther  apart  than 
this,  the  steel  will  deflect  a  dangerous  amount  when  walked  on,  and  will 
leak  snow  and  rain.  Girts  should  be  spaced  for  a  safe  load  of  about  25 
Ibs.  per  square  foot.  From  an  inspection  of  Fig.  112,  it  is  evident  that 
corrugated  steel  lighter  than  No.  24  is  of  little  use  for  mill  buildings. 


*For  details  of  experiments  see  article  by  Ralph  H.  Gage,  in  the  Technograph, 
No.  17. 


232 


CORRUGATED  STEEI, 


Corrugated  steel  of  No.  26  or  28  gage  is  so  thin  that  it  soon  rusts  out 
and  should  never  be  used  unless  for  lining  cheap  buildings. 

Corrugated  Steel  Details.—  Ridge  Roll.—  The  ridge  roll  most 
commonly  used  is  made  from  No.  24  flat  steel,  and  has  a  2^  -inch  roll 
and  6-inch  aprons.  It  comes  in  96-inch  lengths  and  should  be  laid  with 
3  inches  end  lap.  Plain  and  corrugated  ridge  roll  are  used  (see  Fig. 


Ridge  Roll 


PLAIN   RIDGE  CAP. 


CORRUGATED  RIDGE  ROLL. 


Gable  Cornice    Eave  Cornice 


PLAIN   RIDGE  ROLL. 


Flashing  for  Stack 


CORRUGATED  END   WALL   FLASHING. 


Flashing 


[p=-xx-^        r^*s**s 


CORRUGATED  SIDE   FLASHING. 


Outside  Corner  Finish 


FIG.  113. 


FLASHING 


233 


113).    Ridge  roll  is  fastened  with  rivets  or  nails  spaced  6  to  8  inches 
apart. 

Flashing. — Flashing  is  used  where  the  roof  changes  slope,  around 
chimneys  and  openings  in  the  roof,  and  over  windows  and  doors,  and 
should  be  of  sufficient  dimensions  and  so  arranged  that  at  least  3  inches 
vertical  height  is  obtained  between  the  edge  of  the  flashing  and  the 
end  of  the  corrugated  steel  roofing.  Vertical  and  horizontal  seams  of 
all  flashing  should  be  closely  riveted.  Flashing  is  made  from  flat  sheets 


HALF-ROUND  GUTTER;    LAP  JOINT  OR  SLIP  JOINT. 


(d) 


EAVES  TROUGH  HANGERS 

FIG.  114. 


234 


CORRUGATED 


of  the  same  gage  as  the  corrugated  steel,  and  can  be  obtained  up  to  96 
inches  in  length.     Flashing  is  made  both  plain  and  corrugated   (see 

Fig.  113). 

Corner  Finish. — Corner  finish  is  made  in  various  ways,  three  of 
which  are  shown  in  Fig.  113.  Other  methods  are  shown  on  the  suc- 
ceeding pages. 


every  4'-O". 


Hanging  Gutter 


Box  Gutter 


FIG.  116. 


Gutters  and  Conductors. — Gutters  for  eaves  are  ordinarily  made 
from  No.  24,  and  valley  gutters  from  No.  20  galvanized  steel.  Gutters 
may  be  obtained  in  even  foot  lengths  up  to  10  feet,  and  should  have 
4-inch  end  laps.  Special  flat  sheets  up  to  42  inches  in  width  can  be 
obtained  for  making  gutters  and  details. 


CONDUCTORS  AND  GUTTERS 


235 


The  common  sizes  of  half  round  gutters  made  by  the  Garry  Iron 
and  Steel  Roofing  Co.,  Cleveland,  Ohio,  are  shown  in  Fig.  114.  Two 
common  forms  of  adjustable  hangers  are  shown  in  (a)  and  (b)  in 
Fig.  114. 

Two  forms  of  hanging  gutters  are  shown  in  Fig.  115  and  one  form 
of  a  hanging,  and  a  box  gutter  used  with  brick  walls  are  shown  in  Fig. 
116. 

A  standard  form  of  valley  gutter  is  shown  in  Fig.  117.  Extreme 
care  should  be  used  in  making  valley  gutters  to  see  that  the  sides  are 
carried  well  up,  and  that  the  laps  are  well  soldered. 


Va 

Fie 

>• 

^  .. 

1  ley  Gutter 
i.  117. 

Conductors  are  made  plain  round  or  square,  and  corrugated  round 
or  square.  Corrugated  conductors  are  to  be  preferred  to  plain  conduc- 
tors for  the  reason  that  they  will  give  when  the  ice  freezes  inside  of 
them,  and  will  not  burst  as  the  others  often  do.  Common  sizes  of  round 
pipe  are  2",  3",  4",  5",  and  6"  diameter.  Common  sizes  of  square 
pipe  are  i#"  x  2#",  */*"  x  3>4' ',  ^A"  x  4M"  and  3%"  x  5*, 
equal  to  2",  3"  and  4"  round  pipe,  respectively.  Conductor  pipes  are 
fastened  with  hooks  or  by  means  of  wire. 

Design  of  Gutters  and  Conductors. — The  specifications  of  the 
American  Bridge  Company  for  the  design  of  gutters  and  conductors 

are  as  follows: 
17 


236 


CORRUGATED 


Span  of  roof, 
up   to     50' 
50'  to     70' 
70'  to  100' 


Gutter. 
6" 

7" 
8" 


Conductor. 
4"    every  40' 
5"      "      40' 
5"      "      40' 


Hanging  gutters  should  have  a  slope  of  at  least  I  inch  to  15  feet. 
The  diagram  in  Fig.  118  for  the  design  of  gutters  and  conductors 
was  described  in  Engineering  News,  April  17,  1902,  by  Mr.  Emmett 
Steece,  Assoc.  M.  A.  Soc.  C.  E.,  City  Engineer  of  Burlington,  Iowa,  as 
follows : — 


•3" 


Area       in       Plan,       Square       Feet. 

FIG.  118. 


I 

Enej.News 


"The  curves  are  for  %  pitch  or  flat  roofs,  to  full  pitch  or  domes. 
The  areas  are  reduced  to  plan  as  shown.  The  minimum  sizes  of  circu- 
lar and  commercial  rectangular  conductors  are  given  on  the  left  side 
of  the  diagram  and  the  sizes  and  the  minimum  cross-sectional  areas  of 
square  gutters  are  given  on  the  right  hand  side. 

To  use  the  diagram :  Assume  an  area  of  roof,  say  30  x  100  ft.,  or 
3000  sq.  ft.,  y2  pitch  and  one  conductor  for  the  whole  area.  Note  the 
intersection  of  the  vertical  over  area  3000  and  the  curve  of  ^2  pitch; 
following  thence  the  horizontal  line  to  the  left  it  strikes  a  diameter  of  5 
ins.  for  circular,  or  over  3^  x  4^4  ins.  for  commercial  size.  The  next 
larger  size  would  be  used.  The  minimum  cross-sectional  area  of  gut- 
ters is  shown  on  the  right  to  be  about  30  sq.  ins.,  and  the  side  of  a 
square  conductor  about  4.5  ins." 

This  diagram  was  based  on  a  maximum  rainfall  of  1.98  inches 
per  hour. 


CORNICE: 


237 


English  practice  is  as  follows:  Rain-water  or  down-pipes  should 
have  a  bore  or  internal  area  of  at  least  one  square  inch  for  every  60 
square  feet  of  roof  surface  in  temperate  climates,  and  about  35 
square  feet  in  tropical  climates.  They  should  be  placea  not  mor? 
than  20  feet  apart,  and  should  have  gutters  not  less  in  wdth  than 
twice  the  diameter  of  the  pipe. 

The  practice  among  American  architects  is  to  provide  about  one 
square  inch  of  conductor  area  for  each  75  square  feet  of  roof  surface; 
no  conductor  less  than  2  inches  in  diameter  being  used  in  any  case. 

Cornice. — There  are  many  methods  of  finishing  the  gables  and 
eaves  of  buildings.  A  gable  finish  for  a  steel  end,  and  for  a  brick  end 


,-  Roof  5tee/    C/mch  Ftivefj 


L± ±4. 


Roof  J  'fee/  -  ^ 


Cft 


I 
i 

Goble  Rnish  for  Steel  End  Goble  finish  with  Bnck  Wall 

FIG.  119. 


Flashed  Finish 
FIG.  120. 


CORRUGATED  STEEL 


as  used  by  the  American  Bridge  Company,  are  shown  in  Fig.  119.  The 
steel  end  may  have  a  cornice  made  by  bending  the  corrugated  steel  as 
shown,  or  a  molded  cornice. 

The  flashed  finish  shown  in  Fig.  120,  is  used  by  the  American 
Bridge  Company ;  it  is  quite  effective  and  gives  a  very  neat  appearance. 
The  corrugated  steel  siding  should  preferably  be  carried  up  to  the 
roof  steel. 

The  cornice  and  ridge  finish  shown  in  Fig.  121,  designed  by  Mr. 
H.  A.  Fitch,  Minneapolis,  Minn.,  is  very  neat,  efficient  and  economical. 


Section  at  Ridge 


j^!^//=rVU^5 


F/ashinq 


Section  at  Gables  Section  at  Eaves, 

FIG.  121. 

The  galvanized  rivets  are  much  cheaper  than  copper  rivets,  and  are 
preferred  by  many  to  the  copper  rivets.  The  detail  shown  was  for  a 
small  dry  house  in  which  the  eave  strut  was  omitted. 


A/a///ng  sfr/ponenct 
rafter  orenaf  fruss 


Section 


FIG.  122. 


CORNICE 


239 


In  Fig.  122,  the  eave  cornice  is  made  by  simply  extending  the  roof- 
ing steel,  while  the  gable  cornice  is  made  by  bending  a  sheet  of  cor- 
rugated steel  over  the  ends  of  the  purlins  and  nailing  to  wooden  strips 
as  shown. 


\&op  ( 


Section  through 
Gable 


Corner  Finish 


Section  through  Eaves 
FIG.  123. 


The 


Sheets  heavier  than  No.  22  should  not  be  bent  in  the  field, 
corner  finish  is  made  by  bending  a  sheet  of  corrugated  steel. 

In  Fig.  123,  the  eave  and  gable  cornice  are  made  of  plain  flat  steel 
bent  in  the  shop  as  shown.  The  eave  cornice  is  made  to  mitre  with  the 
gable  cornice,  thus  giving  a  neat  finish  at  the  corner.  The  corner  finish 
is  made  by  using  sheets  at  the  corners  in  which  one-half  is  left  plain. 


-N&///ng  strip  on 
end  rafter 


Section  through 

Gable 
.c 

u 


Section  through  Eaves 
FIG.  124. 


240 


CORRUGATED 


In  Fig.  124,  the  eave  strut  and  gable  cornice  are  molded.  The  two 
cornices  are  so  made  as  to  mitre  at  the  corners,  the  mitres  being  made 
in  the  field.  A  plain  corner  cap  is  put  on  as  shown,  after  bending  the 
corrugated  steel  around  the  corner. 


purlin 


strip 


Section  through  Gable 


FIG.  125. 


Bnrctrefs  /8c-c  V_ 
tf*fir*i    ~"^ 

Corn/ce  of*t?4crir 
go/  steel  •  Crimps  4 
Ovtfer  of  *Z4  <ycr/  s 
fastenftf  To  comic 
roofing 

Cor-  wooa  f/7/t 
3/ctthg  of  *^^^?a/ 
3  feel  ,  /+  "corrt/tfa 

"     \ 

n 

ojjo     oj 
oj    o     1 

0 

o 

Section  throuqh  Cornice 

cs 

0 
0 
0 
0 
0 
0 

^  • 

0 

o 
o 

0 
0 

nf>ear\^ 

fee/ 
rctnaf 

•f  » 

cor    _^ 

N 
u 

rr'mpea  cja/-       \ 
ip  tor*2i  ~LS  -A. 
^ 


*10  Ga/  cor  ^5 fee/ 


arxf  r/vef  fo  roofing 


Section  through  Gable 

FIG.  126. 


ANTI-CONDENSATION  ROOFING  241 

In  Fig.  125,  an  eave  purlin  is  used  and  a  channel  is  placed  along 
the  ends  of  the  purlins.  Spiking  strips  should  always  be  used  as  shown, 
and  the  eave  purlin  should  be  fastened  to  the  rafter  by  means  of  angle 
clips. 

The  finish  shown  in  Fig.  126,  was  used  by  the  U.  S.  Government 
and  needs  no  explanation. 

Anti-condensation  Roofing.— To  prevent  the  condensation  of 
moisture  on  the  inner  surface  of  a  steel  roof,  and  the  resulting  dripping, 
the  anti-condensation  roofing  shown  in  Fig.  127  and  in  Fig.  129  is  fre- 
quently used.  The  usual  method  of  constructing  this  roofing  is  as 
follows :  Galvanized  wire  poultry  netting  is  fastened  to  one  eave  purlin 

Asbestos- 

Wire 
Pou/try  Netting 

Anti-Condensation  Roofing 
FIG.  127. 

and  is  passed  over  the  ridge,  stretched  tight  and  fastened  to  the  other 
eave  purlin.  The  edges  of  the  wire  are  woven  together,  and  the  net- 
ting is  fastened  to  the  spiking  strips,  where  used,  by  means  of  small 
staples.  On  the  netting  are  laid  one  or  two  layers  of  asbestos  paper 
i-i6-inch  thick,  and  sometimes  one  or  two  layers  of  tar  paper.  The 
corrugated  steel  is  then  fastened  to  the  purlins  in  the  usual  way. 
Stove  bolts,  3-16"  diameter,  with  I  x  ^  x  4-inch  pflate  washers  on  lower 
side,  are  used  for  fastening  the  side  laps  together  and  for  support- 
ing the  lining  (see  Fig.  129).  The  author  would  recommend  that  pur- 
lins be  spaced  one-half  the  usual  distance  where  anti-condensation  lin- 
ing is  used ;  the  stove  bolts  could  then  be  omitted.  Asbestos  paper  1-16- 
inch  thick  comes  in  rolls,  and  weighs  about  32  pounds  per  square  of  100 
square  feet.  Galvanized  poultry  netting  comes  in  rolls  60  inches  wide 
and  weighs  about  10  pounds  per  square. 

The  corrugated  steel  used  with  anti-condensation  roofing  should 
never  be  less  than  No.  22,  and  the  purlins  should  be  spaced  for  not  less 


CORRUGATED 


-//-0-x<-  /I'-O  ->*  -  -/6-0*- 


j< 60-0 


End  Elevation 


\  Louvres  ! 


/C?  @  9  - 


\4Ji_@9-J>--L. 


6-0 


Wind 
+  -//-J 


i'-!04i 


•'/ff4@4- 


4@\6'-0 


4^-10 


:$  4i@4'-IO\J.@4'9\z^ 
f 


^  5 

I  : 


4@4'0 


-  7- 


Side   Elevation 
FIG.  128.    CORRUGATED  STEEL  PLANS  FOR  A  TRANSFORMER  BUILDING. 


CORRUGATED  STEEL  PLANS 


243 


CorruqoTed       Steel     List   for    Building 


Rectangular  Sheets 


J-S-56  Length 


4-/O 


4- 


s'-y 

S-4" 
6'-Om 
9'-8" 
9'-lO" 


Beveled  Sheets  as  per  Sketch 


U-5-5G 
*Z4- 


7-  is" 
5-9 z" 
4-5  f 


6'-0- 
4-8" 


2--0- 
IO-0" 


7-4- 


& 

^ 

Z*  5 
4*  6 
4-*! 


8 

94-* 
Z*IO  2* 
Z*  II 


Z*ll 


$* 


Z*/Zr? 


84/inea/feet 


'  feer  . 


m 
r      ' 


etfone  coat  FfeafLeatf. 
53 squares  Asbestos.  5heete  16  "w/afe . 

/500  f/n  fr60  "Paul Try  Netting     C err ug&f ions  Zz " 


£nd  tap. 


,-Pou/fry  Neft/ng 


Purlin 


Purlin 


Method  of  Fastening 
Steel  and  Lining  on  Root 


_L- 


Method  of  Fastening 
Steel  on  the  Sides 


-Asbestos 
-Wire  Netting 


Louvers  Mo.  20 


Finish  at  Corner 


Detail  of  Louvres 


FIG.  129.     CORRUGATED  STEEL  LIST  AND  DETAILS  FOR  TRANSFORMER 

BUILDING. 


244  CORRUGATED  STEEL. 

than  30  pounds  per  square  foot.    A  less  substantial  roof  will  not  usually 
be  satisfactory. 

An  engine  house  with  anti-condensation  lining  on  the  roof  and 
sides  has  been  in  use  in  the  Lake  Superior  copper  country  for  several 
years,  and  has  been  altogether  satisfactory  under  trying  conditions. 
The  covering  and  lining  of  roof  and  sides  are  fastened  by  clinch  nails 
to  angle  purlins  and  girts  spaced  about  two  feet  apart. 

A  transformer  building  designed  by  the  author  and  built  by  the 
Gillette-Herzog  Mfg.  Co.,  at  East  Helena,  Montana,  has  anti-condensa- 
tion lining  on  the  roof  as  shown  in  Fig.  129,  and  is  lined  on  the  sides 
with  one  layer  of  asbestos  paper,  and  I  ^4 -inch  No.  26  corrugated  steel. 
The  black  framework,  the  red  side  lining,  and  white  roof  lining  made  a 
very  pleasing  interior.  This  building  after  several  years  is  giving  en- 
tire satisfaction. 

Corrugated  Steel  Plans. — The  shop  plans,  list  of  steel  and  details 
of  the  corrugated  steel  for  a  mill  building  are  shown  in  Fig.  128  and 
Fig.  129  (for  the  general  .plans  and  a  detailed  estimate  of  this  build- 
ing see  Chapter  XXVIII).  Corrugated  steel  sheets  should  be  ordered 
to  cover  three  purlins  or  girts  if  possible.  Bevel  sheets  should  be  ordered 
by  number,  and  sheets  should  be  split  and  reentrant  cuts  should  be  made 
in  the  field.  All  sheets  should  be  plainly  marked  with  the  number  or 
length.  Sheets  No.  22  or  lighter  can  be  bent  in  the  field,  heavier  metal 
should  always  be  bent  at  the  mill.  In  preliminary  estimates  of  corrug- 
ated steel  allow  25  per  cent  for  laps  where  two  corrugations  side  lap 
and  6  inches  end  lap  are  required,  and  15  per  cent  for  laps  where  one 
corrugation  side  lap  and  4  inches  end  lap  are  required. 

Cost  of  Corrugated  Steel. — Galvanized  steel  in  1903  is  quoted  at 
about  75  per  cent  off  the  standard  list,  f .  o.  b.  Pittsburg ;  list  price  of  flat 
galvanized  steel  being  as  follows : 

No.  10  to  16  inclusive   I2c.  per  Ib. 

No.  17  to  21  inclusive    I3C.     "    " 

No.  23  to  24  inclusive    I4c.     "    " 

No.  25  to  26  inclusive    I5c.     "    " 

No.  27    i6c.     "    " 


COST  OF  CORRUGATED  STEEL  245 

The  net  cost  of  corrugated  galvanized  steel  is  found  by  adding  .O5c. 
per  pound  to  the  net  cost  of  flat  galvanized  sheets. 

The  standard  card  of  extras  used  in  1903  is  given  below.    These 
extras  are  to  be  added  to  the  net  price  of  flat  black  or  galvanized  sheets 
to  obtain  the  cost.    These  extras  are  not  subject  to  discount. 
CARD  OF  EXTRAS  FOR  BLACK  OR  GALVANIZED  SHEETS. 

For  corrugating    O5c.  per  Ib. 

For  painting  with  red  oxide loc. 

For  painting  with  Dixon's  graphite 2oc. 

For  painting  with  Goheen's  carbonizing  coating  «3oc. 
For  all   trimmings,  etc.,   flashings,   ridge   caps, 

and  louvres I .  ooc. 

For  flat  sheets  rolled  from  reworked  muck  bar   .  5oc. 

For  sheets  rolled  from  iron  scrap  mixture 2$c. 

For  arches    25c.     "    " 

Black  corrugated  steel  in  1903  is  quoted  about  as  follows,  f.  o.  b, 
Pittsburg: 

No.  16  to  18  inclusive 2.2c.  per  Ib. 

No.  20  to  22  inclusive    2 .  6c. 

No.  24  to  26  inclusive 2.7c. 


CHAPTER  XIX. 
ROOF  COVERINGS. 

Introduction. — Mill  buildings  are  covered  with  corrugated  steel 
supported  directly  on  the  purlins ;  by  slate  or  tile  supported  by  sub- 
purlins;  or  by  corrugated  steel,  slate,  tile,  shingles,  gravel  or  other 
composition  roof,  or  some  one  of  the  various  patented  roofings  sup- 
ported on  sheathing.  The  sheathing  is  commonly  made  of  a  single 
thickness  of  planks,  I  to  3  inches  thick.  The  planks  are  sometimes  laid 
in  two  thicknesses  with  a  layer  of  lime  mortar  between  the  layers  as  a 
protection  against  fire.  In  fireproof  buildings  the  sheathing  is  com- 
monly made  of  reinforced  concrete  constructed  as  described  in  Chapter 
XX.  Concrete  slabs  are  sometimes  used  for  a  roof  covering,  being  in 
that  case  supported  directly  by  the  purlins,  and  sometimes  as  a  sheath- 
ing for  a  slate  or  tile  roof. 

The  roofs  of  smelters,  foundries,  steel  mills,  mine  structures  and 
similar  structures  are  commonly  covered  with  corrugated  steel.  Where 
the  buildings  are  to  be  heated  or  where  a  more  substantial  roof  cov- 
ering is  desired  slate,  tile,  tin  or  a  good  grade  of  composition  roofing 
is  used,  or  the  roof  is  made  of  reinforced  concrete.  For  very  cheap 
and  for  temporary  roofs  a  cheap  composition  roofing  is  commonly  used. 
The  following:  coverings  will  be  described  in  the  order  given;  corrug- 
ated steel,  slate,  tile,  tin,  sheet  steel,  gravel,  slag,  asphalt,  shingle,  and 
also  the  patent  roofings ;  asbestos,  Carey's,  Granite,  Ruberoid  and  Fer- 
roinclave.  The  construction  of  reinforced  concrete  roofing  is  de- 
scribed in  Chapter  XX. 

Corrugated  Steel  Roofing. — Corrugated  steel  roofing  is  laid  on 
plank  sheathing  or  is  supported  directly  on  the  purlins  as  described  in 
Chapter  XVIII.  For  the  cost  of  erecting  corrugated  steel  roofing  see 
Chapter  XXVIII. 


SLATE  ROOFING 


247 


Corrugated  steel  roofing  should  be  kept  well  painted  with  a  good 
paint.  Where  the  roofing  is  exposed  to  the  action  of  corrosive  gases 
as  in  the  roof  of  a  smelter  reducing  sulphur  ores,  ordinary  red  lead  or 
iron  oxide  paint  is  practically  worthless  as  a  protective  coating;  better 
results  being  obtained  with  graphite  and  asphalt  paints.  Graphite  paint 
has  been  quite  extensively  used  for  painting  corrugated  steel  in  the 
Butte,  Mont.,  district.  The  corrosion  of  corrugated  steel  is  sometimes 
very  rapid.  In  1898  the  author  saw  at  the  Trail  Smelter,  Trail,  B.  C., 
a  corrugated  steel  roof  made  of  No.  22  corrugated  steel  and  painted 
with  oxide  of  iron  paint  that  had  corroded  so  badly  in  one  year  that 
one  could  stick  his  finger  through  it  as  easily  as  through  brown  paper. 
The  climate  in  that  locality  is  moist  and  the  smelter  was  used  for  re- 
ducing sulphur  ores.  Galvanized  corrugated  steel  is  quite  extensively 
used  in  the  Lake  Superior  district. 

Slate  Roofing. — There  are  many  varieties  of  roofing  slate,  among 
which  the  Brownville  and  Monson  slates  of  Maine,  and  the  Bangor 
and  Peach  Bottom  slates  of  Pennsylvania  are  well  known  and  are  of 


Gage;       , 


JUULJUU 

FIG.  130. 


excellent  quality.  Besides  the  characteristic  slaty  color,  green,  purple, 
red  and  variegated  roofing  slates  may  be  obtained.  The  best  quality 
of  slate  has  a  glistening  semi-metallic  appearance.  Slate  with  a  dull 


248  ROOF  COVERINGS 

earthy  appearance  will  absorb  water  and  is  liable  to  be  destroyed  by 
the  frost. 

Roofing  slates  are  usually  made  from  J^  to  l/4  inches  thick;  3-16- 
inch  being  a  very  common  thickness.  Slates  vary  in  size  from  6"  x  12" 
to  24"  x  44" ;  the  sizes  varying  from  6"  x  12"  to  12"  x  18"  being  the 
most  common. 

Slates  are  laid  like  shingles  as  shown  in  Fig.  130.  The  lap  most 
commonly  used  is  3  inches ;  where  less  than  the  minimum  pitch  of  Y±  is 
used  the  lap  should  be  increased. 

The  number  of  slates  of  different  sizes  required  for  one  square  of 
100  square  feet  of  roof  for  a  3-inch  lap  are  given  in  Table  XIX. 

The  weight  of  slates  of  the  various  lengths  and  thicknesses  required 
for  one  square  of  roofing,  using  a  3-inch  lap  is  given  in  Table  XX. 
The  weight  of  slate  is  about  174  pounds  per  cubic  foot. 

The  weight  of  slate  per  superficial  square  foot  for  different  thick- 
nesses is  given  in  Table  XXI. 

The  minimum  pitch  recommended  for  a  slate  roof  is  Y±  ;  but  even 
with  steeper  slopes  the  rain  and  snow  may  be  driven  under  the  edges 
of  the  slates  by  the  wind.  This  can  be  prevented  by  laying  the  slates 
ii\  slater's  cement.  Cemented  joints  should  always  be  used  around  eaves, 
ridges  and  chimneys. 

Slates  are  commonly  laid  on  plank  sheathing.  The  sheathing  should 
be  strong  enough  to  prevent  deflections  that  will  break  the  slate,  and 
should  be  tongued  and  grooved,  or  shiplapped,  and  dressed  on  the  upper 
surface.  Concrete  sheathing  reinforced  with  wire  lath  or  expanded 
m^tai  is  now  being  used  quite  extensively  for  slate  and  tile  roofs,  and 
makes  a  fireproof  roof.  Tar  roofing  felt  laid  between  the  slates  and 
the  sheathing  assists  materially  in  making  the  roof  waterproof,  and 
prevents  breakage  when  the  roof  is  walked  on.  The  use  of  rubber- 
soled  shoes  by  the  workmen  will  materially  reduce  the  breakage  caused 
by  walking  on  the  roof.  Roofing  slates  may  also  be  supported  directly 
on  laths  or  sub-purlins.  The  details  of  this  method  are  practically 
the  same  as  for  tile  roofing,  which  see. 


TABLES 


249 


TABLE  XIX. 
NUMBER  OF  ROOFING  SLATES  REQUIRED  TO  LAY  ONE  SQUARE  OF  ROOF  WITH 

3-INCH    LAP. 


Size  in 
Inches. 

No.  of 
Slate  in 
Square. 

Size  in 
Inches. 

No  of 
Slate  in 
Square. 

Size  in 
Inches. 

No.  of 
Slate  in 
Square. 

6X12 

533 

8x16 

277 

12x20 

141 

7  12 

457 

9  16 

246 

14  20 

121 

8  12 

400 

10  16 

221 

11  22 

137 

&  12 

355 

12  16 

184 

12  22 

126 

10  12 

320 

9  18 

213 

14  22 

108 

12  12 

266 

10  18 

192 

12  24 

114 

7  14 

374 

11  18 

174 

14  24 

98 

8  14 

327 

12  18 

160 

16  24 

86 

9  14 

291 

14  18 

137 

14  26 

89 

10  14 

261 

10  20 

169 

16  26 

78 

12  14 

218 

11  20 

154 

TABLE  XX. 

THE  WEIGHT  OF  SLATE  REQUIRED  FOR  ONE  SQUARE  OF  ROOF. 


Length 


Weight  in  pounds,  per  square,  for  the  thickness. 


in 
Inches. 

W 

3  » 
16 

U' 

K* 

w 

5/s* 

M" 

I* 

12 

483 

724 

967 

1450 

1936 

2419 

2902 

3872 

14 

460 

688 

920 

1370 

1842 

2301 

2760 

3683 

16 

445 

667 

890 

1336 

1784 

2229 

2670 

3567 

18 

434 

650 

869 

1303 

1740 

2174 

2607 

3480 

20 

425 

637 

851 

1276 

1704 

2129 

2553 

3408 

22 

418 

626 

836 

1254 

1675 

2093 

2508 

3350 

24 

412 

617 

825 

1238 

1653 

2066 

2478 

3306 

26 

407 

610 

815 

1222 

1631 

2039 

2445 

3263 

TABLE  XXI. 
WEIGHT  OF  SLATE  PER  SQUARE  FOOT. 


Thickness—  in  

^ 

13<T 

u 

H 

Yz 

% 

M 

1 

Weight—  Ibs  

1.81 

2.71 

3.62 

5.43 

7.25 

9.06 

10.87 

14.5 

j-L 

250  ROOF  COVERINGS 

When  roofing  slates  are  laid  on  sheathing  they  are  fastened  by 
two  nails,  one  in  each  upper  corner.  When  supported  directly  on  sub- 
purlins  the  slates  are  fastened  by  copper  or  composition  wire.  Gal- 
vanized and  tinned  steel  nails,  copper,  composition  and  zinc  slate  roofing 
nails  are  used.  Where  the  roof  is  to  be  exposed  to  corrosive  gases  cop- 
per, composition  or  zinc  nails  should  be  used. 

Slate  roofs  when  made  from  first  class  slates  well  laid  have  been 
known  to  last  50  years.  When  poorly  put  on  or  when  an  inferior  qual- 
ity of  slate  is  used  slate  roofs  are  comparatively  short-lived.  Slates  are 
easily  broken  by  walking  over  the  roof  and  are  sometimes  broken  by 
hailstones.  Slate  roofing  is  fireproof  as  far  as  sparks  are  concerned, 
but  the  slates  will  crack  and  disintegrate  when  exposed  to  heat.  Local 
conditions  have  much  to  do  with  the  life  of  slate  roofs ;  an  ordinary  life 
being  from  25  to  30  years. 

First  class  slate  3-16  to  Y^  inches  thick  may  ordinarily  be  obtained 
f .  o.  b.  at  the  quarry  for  from  $5 .  oo  to  $7 .  oo  per  square ;  common 
slate  for  from  $2.00  to  $4.00  per  square ;  while  extra  fine  slate  may 
cost  from  $10.00  to  $12.00  per  square. 

An  experienced  roofer  can  lay  from  il/2  to  2  squares  of  slate  in  a 
day  of  10  hours.  In  1903  slater's  supplies  were  quoted  as  follows: 
Galvanized  iron  nails,  2l/2  to  3  cents  per  Ib. ;  copper  nails,  20  cents  per 
Ib. ;  zinc  nails,  10  cents  per  Ib. ;  slater's  felt,  70  to  75  cents  per  roll  of 
500  square  feet ;  two-ply  tar  roofing  felt,  75  cents  per  square ;  slater's 
cement  in  lo-lb.  kegs,  10  cents  per  Ib. 

Trautwine  gives  the  cost  of  slate  roofs  as  $7.00  per  square  and 
upwards.  The  costs  of  slate  roofs  per  square  is  given  in  the  reports  of 
the  Association  of  Railway  Superintendents  of  Bridges  and  Buildings, 
as  follows:  New  England,  $9.00  to  $12.00;  New  York,  $9.00  to 
$10.00;  Virginia  $4. 10  to  $5.00;  California,  $10.00  to  $10.50. 

Tile  Roofing. — Baked  clay  or  terra-cotta  roofing  tiles  are  made 
in  many  forms  and  sizes.  Plain  roofing  tiles  are  usually  iol/2  inches 
long,  6l/4  inches  wide  and  ^  inches  thick ;  weigh  from  2  to  2l/2  pounds 
each  and  lay  one-half  to  the  weather.  There  are  many  other  forms  of 


TIN  ROOFS  25 1 

tile  among  which  book  tile,  Spanish  tile,  pan  tile  and  Ludowici  tile 
are  well  known.  Tiles  are  also  made  of  glass  and  are  used  in  the  place 
of  skylights. 

Tiles  may  be  laid  (i)  on  plank  sheathing,  (2)  on  concrete  and  ex- 
panded metal  or  wire  lath  sheathing,  or  (3)  may  be  supported  directly 
on  angle  sub-purlins  as  shown  in  Fig.  87.  Tiles  are  laid  on  sheathing 
in  the  same  manner  as  slates. 

The  roof  shown  in  Fig.  87  was  constructed  as  follows:  Terra- 
cotta tiles,  manufactured  by  the  Ludowici  Roofing  Tile  Co.,  Chicago,  111., 
were  laid  directly  on  the  angle  sub-purlins,  every  fourth  tile  being  se- 
cured to  the  angle  sub-purlins  by  a  piece  of  copper  wire.  The  tiles  were 
interlocking,  requiring  no  cement  except  in  exceptional  cases.  The  tiles 
were  9  x  16  inches  in  size ;  135  being  sufficient  to  lay  a  square  of  100 
square  feet  of  roof.  These  tiles  weigh  from  750  to  800  Ibs.  per  square, 
and  cost  about  $6.00  per  square  at  the  factory.  Skylights  in  this  roof 
were  made  by  substituting  glass  tiles  for  the  terra-cotta  tiles.  This  and 
similar  tile  has  been  used  in  this  manner  on  a  large  number  of  mills  and 
train  sheds  with  excellent  results. 

Tile  roofs  laid  without  sheathing  do  not  ordinarily  condense  the 
steam  on  the  inner  surface  of  the  roof  unless  the  tiles  are  glazed,  al- 
though several  cases  have  been  brought  to  the  author's  attention  where 
the  condensation  has  caused  trouble  with  tile  roofs  made  of  porous 
tiles.  Anti-condensation  roof  lining  should  be  used  where  there  is  dan- 
ger of  excessive  sweating,  or  a  porous  tile  should  be  used  that  is  known 
to  be  non-sweating.  The  cost  of  tile  roofing  varies  so  much  that  general 
costs  are  practically  worthless.  The  reports  of  the  Association  of  Rail- 
way Superintendents  of  Bridges  and  Buildings  give  the  cost  in  New 
England  as  from  $30.00  to  $33.00  per  square. 

Tin  Roofs. — Tin  plates  are  made  by  coating  flat  iron  or  steel  sheets 
with  tin,  or  with  a  mixture  of  lead  and  tin.  The  former  is  called 
"bright"  tin  plate  and  the  latter  "terne"  plate.  Terne  plates  should  not 
be  used  where  the  roof  will  be  subjected  to  the  action  of  corrosive  gases 

for  the  reason  that  the  lead  coating  is  rapidly  destroyed.     Plates  are 
18 


252  ROOF  COVERINGS 

covered  with  tin  (i)  by  the  dipping  process  in  which  the  plates  are 
pickled  in  dilute  sulphuric  acid,  annealed,  again  pickled,  dipped  in  palm 
oil  and  then  in  a  bath  of  molten  tin  or  tin  and  lead ;  or  ^2)  by  the  roller 
process  in  which  the  plates  are  run  through  rolls  working  in  a  large 
vessel  containing  oil,  immediately  after  being  dipped.  The  latter 
method  gives  the  better  results. 

Two  sizes  of  tin  plates  are  in  common  use,  14"  x  20"  and  20"  x 
28",  the  latter  size  being  most  used.  Tin  sheets  are  made  in  several 
thicknesses,  the  1C,  or  No.  29  gage  weighing  8  ounces  to  the  square 
foot,  and  the  IX,  or  No.  27  gage  weighing  10  ounces  to  the  square  foot, 
being  the  most  used.  The  standard  weight  of  a  box  of  112  sheets,  14  x 
20  size  is  1 08  pounds  for  1C  plate,  and  136  pounds  for  IX  plate.  Boxes 
containing  imperfect  sheets  or  "wasters"  are  marked  ICW  or  IXW. 
Every  sheet  should  be  stamped  with  the  name  of  the  brand  and  the 
thickness. 

The  value  of  tin  roofing  depends  upon  the  amount  of  tin  used  in 
coating  and  the  uniformity  with  which  the  iron  has  been  coated.  The 
amount  of  tin  used  varies  from  8  to  47  pounds  for  a  box  of  20  x  28  size 
containing  112  sheets. 

Tin  roofing  is  laid  (i)  with  a  flat  seam,  or  (2)  with  a  standing 
seam.  In  the  former  method  the  sheets  of  tin  are  locked  into  each 
other  at  the  edges,  the  seam  is  flattened  and  fastened  with  tin  cleats 
or  is  nailed  firmly  and  is  soldered  water  tight.  Rosin  is  the  best  flux 
for  soldering,  although  some  tinners  recommend  the  use  of  diluted 
chloride  of  zinc.  For  flat  roofs  the  tin  should  be  locked  and  soldered 
at  all  joints,  and  should  be  secured  by  tin  cleats  and  not  by  nails.  For 
steep  roofs  the  tin  is  commonly  put  on  with  standing  seams,  not 
soldered,  running  with  the  pitch  of  the  roof,  and  with  cross-seams 
double  locked  and  soldered.  One  or  two  layers  of  tar  paper  should 
be  placed  betwen  the  sheathing  and  the  tin. 

In  painting  tin  all  traces  of  grease  and  rosin  should  be  removed, 
benzine  or  gasoline  being  excellent  for  this  purpose.  A  paint  composed 
of  10  pounds  Venetian  red  and  one  pound  red  lead  to  one  gallon  of 


SHEET  STEEL  ROOFING  253 

pure  linseed  oil  is  recommended.  The  under  side  of  the  sheets  should 
be  painted  before  laying.  Tin  roofs  should  be  painted  every  two  or 
three  years.  If  kept  well  painted  a  tin  roof  should  last  25  to  30  years. 

For  flat  seam  roofing,  using  y2-mch  locks,  a  box  of  14  x  20  tin 
will  cover  192  square  feet,  and  for  standing  seam,  using  ^-inch  locks 
and  turning  1^4  and  1^2  -inch  edges,  making  i-inch  standing  seams,  it 
will  lay  1 68  square  feet.  For  flat  seam  roofing,  using  ^-inch  locks, 
a  box  of  20  x  28  tin  will  lay  about  399  square  feet,  and  for  standing 
seam,  using  ^-inch  locks  and  turning  i*4  and  i^-inch  edges,  making 
I -inch  standing  seams,  it  will  lay  about  365  square  feet. 

Current  prices  in  1903  for  tin  in  small  quantities  were  about  as 
follows : 

American  Charcoal  Plates: 

1C,    14x20 $5. 50  to  $6. 50  per  box  of  112  sheets; 

IX,    14x20 $6. 60  to  $8. 25  per  box  of  112  sheets. 

American  Coke  Plates,  Bessemer : 

1C,    14x20 $4. 70  to  $4. 80 per  box  of  112  sheets; 

IX,  14x20 $6. 60  to  $8. 25  per  box  of  112  sheets. 

American  Terne  Plates: 

1C,  20x28 $  9.50; 

IX,  20x28 $11.50. 

Two  good  workmen  can  put  on  and  paint  from  2^2  to  3  squares 
of  tin  roofing  in  8  hours.  Tin  roofs  cost  from  $7.00  to  $11.00  or 
$12.00  per  square  depending  upon  the  specifications  and  the  cost  of 
labor. 

Sheet  Steel  Roofing. — Sheet  steel  roofing  is  sold  in  sheets  28 
inches  wide  and  from  4  to  12  feet  long,  or  in  rolls  26  inches  wide  and 
about  50  feet  long.  It  is  commonly  laid  with  vertical  standing  seams 
and  horizontal  flat  seams;  tin  cleats  from  12  to  15  inches  apart  being 
nailed  to  the  plank  sheathing  and  locked  into  the  seams.  Sheet  steel 
plates  are  also  made  with  standing  crimped  seams  near  the  edges,  which 
are  nailed  to  V-shaped  sticks;  the  horizontal  seams  being  made  by 
lapping  about  6  inches. 


254 


ROOF  COVERINGS 


Care  should  be  used  in  laying  sheet  steel  roofing  to  see  that  it  does 
not  come  in  contact  with  materials  containing  acids,  and  it  should  be 
kept  well  painted.  The  weight  of  flat  steel  of  different  gages  is  given 
in  Table  XV.  Nos.  26  and  28  gage  sheets  are  commonly  used  for  sheet 
steel  roofing.  No.  26  black  sheet  steel  was  quoted  in  1903  at  about 
$3.20  per  100  pounds,  and  No.  26  galvanized  sheet  steel  at  about  $4.00 
per  100  pounds  in  small  lots.  Sheet  steel  roofing  can  be  laid  at  a 
somewhat  less  cost  than  tin  roofing. 

Gravel  Roofing. — Gravel  roofing  is  made  by  laying  and  firmly 
nailing  several  layers  of  roofing  felt  on  sheathing  so  as  to  break  joints 
from  9  to  12  inches ;  the  laps  are  mopped  and  cemented  together  with 
roofing  cement  or  tar,  and  finally  the  entire  surface  is  covered  with  a 
good  coating  of  hot  cement  or  tar.  The  cement  or  tar  should  not  be 
hot  enough  to  injure  the  fibre  of  the  felt.  While  the  cement  or  tar 
is  still  hot  the  surface  of  the  roof  is  covered  with  a  layer  of  clean  gravel 
that  has  been  screened  through  a  ^g-inch  mesh.  It  requires  from  8  to 
10  gallons  of  tar  or  cement  and  about  %  of  a  yard  of  gravel  per  square 
of  100  square  feet  of  roof.  When  the  roof  is  to  be  subjected  to  the 
action  of  corrosive  gases  it  should  be  flashed  with  copper  or  composi- 
tion, or  the  flashing  may  be  made  of  felt.  The  number  of  layers  of  felt 
varies  with  the  conditions,  but  should  never  be  less  than  four  (4-ply). 

The  details  of  laying  gravel  roofs  differ  and  it  is  impossible  to 
do  more  than  give  a  few  standard  specifications.  The  following  specifi- 
cations are  about  standard  in  the  West.  In  writing  specifications  for 
four-ply  gravel  roofing  omit  one  layer  of  roofing  felt  in  the  specifications 
for  five-ply  gravel  roofing.  Three-ply  roofing  is  sometimes  used  for 
temporary  structures. 

Five  (5)  Ply  Wool  Felt,  Composition  and  Gravel  Roof. — First 
cover  the  sheathing  boards  with  one  (i)  layer  of  dry  felt  and  over 
this  put  four  (4)  thicknesses  of  wool  roofing  felt,  weighing  not  less  than 
fifteen  (15)  pounds  (single  thickness)  to  the  square  of  one  hundred 
(100)  feet.  This  felt  to  be  smoothly  and  evenly  laid  and  well  cemented 
together  the  full  width  of  the  lap,  not  less  than  nine  (9)  inches  between 
each  layer,  with  best  roofing  cement  or  refined  tar,  using  not  less  than 


GRAVEL  ROOFING  255 

one  hundred  (100)  pounds  of  roofing  cement  or  tar  to  the  square  of 
one  hundred  (100)  feet.  All  joinings  along  walls  and  around  openings 
to  be  carefully  made.  The  roof  to  be  then  covered  with  a  heavy  coating 
of  roofing  cement  or  tar  and  screened  gravel,  not  less  than  one  (i)  cubic 
yard  of  gravel  to  six  hundred  (600)  square  feet,  gravel  to  be  screened 
through  y&  -inch  mesh  and  free  from  sand  and  loam.  All  walls  and 
openings  to  be  flashed.  All  roofing  cement  and  tar  is  to  be  applied  hot. 

Six  (6)  Ply  Cap  Sheet  Wool  Felt,  Composition  and  Gravel  Roof. 
— First  cover  the  sheathing  boards  with  one  (i)  layer  of  dry  felt  and 
over  this  put  four  (4)  thicknesses  of  wool  roofing  felt,  weighing  not 
less  than  fifteen  (15)  pounds  (single  thickness)  to  the  square  of  one 
hundred  (100)  feet.  This  felt  to  be  smoothly  and  evenly  laid  and  well 
cemented  together  the  full  width  of  the  lap,  not  less  than  nine  (9) 
inches  between  each  layer,  with  best  roofing  cement  or  refined  tar,  using 
not  less  than  one  hundred  and  twenty  (120)  pounds  of  roofing  cement 
or  tar  to  the  square  of  one  hundred  (100)  feet.  The  entire  surface  then 
to  be  mopped  over  with  roofing  cement  or  tar  and  a  cap  sheet  of  wool 
felt  applied.  All  joinings  along  the  walls  and  around  the  openings  to 
be  carefully  made.  The  roof  to  be  then  covered  with  a  heavy  coating 
of  roofing  cement  or  tar  and  screened  gravel,  not  less  than  one  (i) 
cubic  yard  of  gravel  to  six  hundred  (600)  square  feet,  gravel  to  be 
screened  through  ^-inch  mesh  and  free  from  sand  and  loam.  All  walls 
and  openings  to  be  flashed.  All  roofing  cement  and  tar  shall  be  ap- 
plied hot. 

Six  (6)  Ply  Combined  Flax  and  Wool  Felt,  Composition  and 
Gravel  Roof. — First  cover  the  sheathing  boards  with  one  (i)  layer  of 
dry  felt  and  over  this  put  one  ( I )  layer  of  flax  felt  and  three  thicknesses 
of  wool  roofing  felt,  weighing  not  less  than  fifteen  (15)  pounds  (single 
thickness)  to  the  square  of  one  hundred  (100)  feet.  This  felt  to  be 
smoothly  and  evenly  laid  and  well  cemented  together  the  full  width 
of  the  lap,  not  less  than  eleven  (n)  inches  between  each  layer,  with  best 
roofing  cement  or  refined  tar,  using  not  less  than  one  hundred  and 
twenty  (120)  pounds  of  roofing  cement  or  tar  to  the  square  of  one 
hundred  (100)  feet.  The  entire  surface  then  to  be  mopped  over  with 
roofing  cement  or  tar  and  a  cap  sheet  of  wool  felt  applied.  All  joinings 
along  walls  and  around  openings  to  be  carefully  made.  The  roof  to 
be  then  covered  with  a  heavy  coating  of  roofing  cement  or  tar  and 
screened  gravel,  not  less  than  one  ( i )  cubic  yard  of  gravel  to  six  hun- 
dred (600)  square  feet,  gravel  to  be  screened  through  ^-inch  mesh  and 


256  ROOF  COVERINGS 

free  from  sand  and  loam.  All  walls  and  openings  to  be  flashed.  All 
roofing  cement  and  tar  shall  be  applied  hot. 

In  Building  Construction  and  Superintendence,  Part  II,  Kidder 
gives  the  following  specifications  for  flashing  a  gravel  roof: 

"Flashing. — Finish  the  roofing  against  fire  walls,  chimneys,  scuttle 
and  skylight  by  turning  the  felt  up  4  inches  against  the  wall.  Over 
this  lay  an  8-inch  strip  of  felt  with  half  its  width  on  the  roof.  Fasten 
the  upper  edge  of  the  strip  and  the  several  layers  of  felt  to  the  wall 
by  laths  or  wooden  strips  securely  nailed,  and  press  the  strip  of  felt 
into  the  angle  of  the  wall  and  cement  to  the  roof  with  hot  pitch.  Nail 
the  lower  edge  of  the  strip  to  the  roof  every  4  or  5  inches.  Take  spe- 
cial care  in  fitting  around  chimneys  and  skylights.  Extend  the  felt  up 
6  inches  on  the  pitch  of  the  roof,  and  secure  every  4  inches  with  3d 
nails  with  tin  washers." 

The  pitch  should  not  be  more  than  %  and  should  preferably  be 
about  24  to  i  inch  to  the  foot.  Gravel  is  sometimes  used  on  roofs 
nearly  flat. 

Gravel  roofing  under  ordinary  conditions  will  last  for  from  10  to 
15  years.  With  careful  attention  it  can  be  made  to  last  longer  and  has 
been  known  to  last  30  years. 

The  cost  of  gravel  roofing  varies  with  local  conditions  and  speci- 
fications. In  various  reports  of  the  Association  of  Railway  Superintend- 
ents of  Bridges  and  Buildings  costs  of  gravel  roofs,  not  including  the 
sheathing,  per  square  are  given  as  follows:  Three-ply  gravel  roof  in 
California,  costs  $3.75 ;  four-ply  (4)  gravel  roof  in  Kansas,  costs  $3.00 ; 
in  Chicago,  costs  from  $3.00  to  $4.00;  and  in  New  England,  costs 
from  $4.00  to  $5.00.  The  cost  varies  greatly  with  the  specifications. 

Prepared  Gravel  Roofing. — Prepared  gravel  roofings  may  be  bought 
in  the  market.  Prepared  gravel  roofing  manufactured  by  the  Armitage 
Manufacturing  Company,  Richmond,  Va.,  was  quoted  at  $2.50  per 
roll  of  1 08  square  feet  and  including  nails  and  cement,  delivered  in  cen- 
tral Illinois.  This  company  has  discontinued  the  manufacture  of  pre- 
pared slag  roofing. 

Slag  Roofing. — Slag  is  sometimes  used  in  the  place  of  gravel  in 
making  roofs.  The  method  of  constructing  the  roof  and  the  specifica- 


ASPHAI/T  ROOFING  257 

tions  are  essentially  the  same  as  for  a  gravel  roof.  For  detailed  specifi- 
cations for  laying  slag  roofing  see  description  of  the  Locomotive  Erect- 
ing and  Machine  Shop,  Philadelphia  &  Reading  R.  R.,  given  in  Part 
IV. 

Asphalt  Roofing. — Asphalt  roofing  is  laid  like  tar  and  gravel  roof- 
ing except  that  asphalt  is  used  in  the  place  of  tar  or  cement.  For  dis- 
cussion of  the  composition  and  properties  of  asphalt  see  Baker's  Roads 
and  Pavements,  Chapter  XIII.  The  following  specifications  will  give 
a  good  roof: 

Five  (5)  Ply  Wool  Felt,  Trinidad  Asphalt  and  Gravel  Roof.— 'First 
cover  the  sheathing  boards  with  one  ( i )  thickness  of  dry  felt,  and  over 
this  put  four  (4)  thicknesses  of  No.  I  wool  roofing  felt,  weighing  not 
less  than  fifteen  (15)  pounds  (single  thickness)  to  the  square  of  one 
hundred  ( 100)  square  feet.  The  felt  to  be  smoothly  and  evening  laid, 
and  well  cemented  together  the  full  width  of  the  lap,  rot  less  than  nine 
(9)  inches  between  each  layer,  with  Trinidad  asphalt  roofing  cement, 
using  not  less  than  one  hundred  ( 100)  pounds  of  asphalt  to  one  square 
of  one  hundred  (100)  square  feet.  All  joinings  along  the  wall  and 
around  openings  to  be  carefully  made.  The  roof  is  then  to  be  cov- 
ered with  a  coating  of  asphalt  and  screened  gravel,  not  less  than  one 
(i)  cubic  yard  of  gravel  to  six  hundred  (600)  square  feet  of  roof, 
gravel  to  be  screened  through  a  ^-inch  mesh  and  to  be  free  from 
loam.  All  walls  to  be  flashed  with  old  style  tin  or  galvanized  iron,  or 
a  2  x  4  is  to  be  built  into  the  walls  to  make  roof  connections  to. 

Five  (5)  Ply  Combined  Flax  and  Wool  Felt,  Trinidad  Asphalt  and 
Gravel  Roof. — First  cover  the  sheathing  boards  with  one  thickness  of 
dry  felt,  over  this  put  one  (i)  thickness  of  flax  felt  and  three  (3)  thick- 
nesses of  No.  i  wool  roofing  felt,  weighing  not  less  than  fifteen  (15) 
pounds  (single  thickness)  to  the  square  of  one  hundred  (100)  square 
feet.  The  felt  to  be  smoothly  and  evenly  laid,  and  well  cemented  to- 
gether the  full  width  of  the  lap,  not  less  than  eleven  (n)  inches  be- 
tween each  layer,  with  Trinidad  asphalt  roofing  cement,  using  not  less 
than  one  hundred  (100)  pounds  of  asphalt  to  the  square  of  one  hun- 
dred (100)  square  feet.  All  joinings  along  the  walls  and  around  open- 
ings to  be  carefully  made.  The  roof  is  then  to  be  covered  with  a  coat- 
ing of  Trinidad  asphalt  roofing  cement  and  screened  gravel,  not  less 
than  one  (i)  cubic  yard  of  gravel  to  six  hundred  (600)  square  feet 


258  ROCF  COVERINGS 

of  roof,  gravel  to  be  screened  through  a  ^6 -inch  mesh  and  to  be  free 
from  loam.  All  walls  to  be  flashed  with  old  style  tin  or  galvanized 
iron,  or  a  2  x  4  is  to  be  built  into  the  wall  to  make  connections  to. 

Prepared  asphalt  roofing  can  be  bought  in  the  market.  It  is  sold 
in  rolls  36  inches  wide  and  is  laid  in  courses. 

The  Arrow  Brand- Ready  Asphalt  Roofing,  manufactured  by  the 
Asphalt  Ready  Roofing  Company,  New  York,  was  quoted  in  1903  de- 
livered in  central  Illinois  as  follows:  Arrow  Brand  No.  I,  sand  sur- 
faced, per  roll  $2.75;  rolls  contain  no  square  feet  which  will  cover 
100  square  feet  of  roof  and  weigh  80  pounds.  Arrow  Brand  No.  2, 
gravel  surfaced,  per  roll  $2.75 ;  rolls  contain  no  square  feet  which  will 
cover  100  square  feet  of  roof  and  weigh  140  pounds.  The  necessary 
nails  and  asphalt  required  in  laying  the  roofing  are  included  in  the 
above  prices.  This  roofing  is  in  use  by  a  number  of  railways. 

Shingle  Roofs. — Shingle  roofs  are  now  very  seldom  used  for  mill 
buildings.  Shingles  have  an  average  width  of  4  inches  and  with  4 
inches  laid  to  the  weather  900  are  required  to  lay  one  square  of  roof. 
One  thousand  shingles  require  about  5  Ibs.  of  nails.  One  man  can  lay 
from  1500  to  2000  shingles  in  a  day  of  8  hours.  The  cost  of  shingle 
roofs  varies  with  the  locality  from,  say,  $3.25  to  $6.25  per  square. 

Asbestos  Roofing. — The  "Standard"  Asbestos  Roofing,  manufac- 
tured by  the  H.  W.  Johns-Manville  Co.,  New  York,  is  composed  of  a 
strong  canvas  foundation  with  asbestos  felt  on  the  under  side,  and  sat- 
turated  asbestos  felt  on  the  upper  side  finished  with  a  sheet  of  plain 
asbestos ;  the  whole  being  cemented  together  with  a  special  cement  and 
compressed  together  into  a  flexible  roofing.  It  does  not  require  paint- 
ing, although  it  is  commonly  painted  with  a  special  paint,  one  gallon 
of  which  will  cover  about  150  square  feet.  The  roofing  is  laid  with  a 
lap  of  2  inches,  beginning  at  the  lower  edge  of  the  roof  and  running 
parallel  to  the  eaves.  The  laps  are  cemented  and  are  nailed  with  special 
roofing  nails  and  caps.  The  roofing  is  laid  on  sheathing  and  is  very 
easily  and  cheaply  laid.  It  is  quite  flexible  and  may  be  used  for  flash- 
ing and  for  gutters.  It  is  practically  fireproof  and  makes  a  very  satis- 
factory roof.  Asbestos  roofing  comes  in  rolls  and  weighs  about  75 


PATENT  ROOFINGS  259 

pounds  per  square.    It  costs  about  $3.00  per  square  laid  on  the  roof. 

The  above  named  company  makes  several  other  brands  of  asbestos 
roofing  the  cost  of  which  is  about  the  same  as  the  "Standard." 

Asbestos  roofing  felts  may  be  purchased  which  are  used  for  roof- 
ing in  one,  two  or  three-ply,  and  are  laid  in  the  same  way  as  for  gravel 
roofing. 

Carey's  Roofing. — Carey's  Magnesia  Flexible  Cement  Roofing, 
manufactured  by  the  Philip  Carey  Manufacturing  Company,  Lockland, 
Ohio,  is  made  by  putting  a  layer  of  asphalt  cement  composition  on  a 
foundation  of  woolen  felt  and  imbedding  a  strong  burlap  in  the  upper 
surface  of  the  cement.  After  laying,  the  burlap  is  covered  with  a  tough 
elastic  paint  which  when  it  dries  gives  a  surface  similar  to  slate.  The 
roof  is  practically  acid  proof  and  burns  very  slowly.  It  comes  in  rolls 
29  inches  wide  and  containing  sufficient  material  to  lay  one  square  of 
roof.  The  roofing  is  made  in  two  weights,  standard  weighing  90 
pounds  per  square,  and  extra  heavy  weighing  about  115  pounds  per 
square.  A  special  flap  is  provided  on  one  side  to  cover  the  nail  heads. 
The  roofing  is  very  pliable  and  can  be  used  for  flashing  and  for  gutters. 
It  should  be  laid  on  sheathing  and  is  very  easily  and  cheaply  applied. 
It  may  be  laid  over  an  old  shingle  or  corrugated  iron  roof.  It  costs 
about  $2.75  to  $3.25  per  square  laid  on  the  roof. 

Granite  Roofing. — Granite  Roofing,  manufactured  by  the  Eastern 
Granite  Roofing  Company,  New  York,  is  a  ready-to-lay  composition 
roofing  with  manufactured  quartz  pebbles  imbedded  in  its  upper  sur- 
face. It  is  a  very  satisfactory  roofing  and  is  quite  extensively  used.  It 
costs  about  $2 . 75  to  $3 . 75  per  square  laid  on  the  roof. 

Ruberoid  Roofing. — P.  &  B.  Ruberoid  Roofing,  manufactured  by 
the  Standard  Paint  Co.,  New  York,  is  quite  extensively  used  and  has 
given  good  satisfaction.  The  following  description  is  taken  from  the 
maker's  catalog:  "No  paper  whatever  is  used  in  the  manufacture  of 
Ruberoid  Roofing.  It  has  a  foundation  of  the  best  wool  felt,  except 
in  the  case  of  the  ^2 -ply  grade  which  is  a  combination  of  wool  and  hair. 
This  is  first  saturated  with  the  P.  &  B.  water  and  acid  proof  compound, 


260  ROOF  COVERINGS 

and  afterwards  coated  with  a  hard  solution  of  the  same  material,  there- 
by making  the  roofing  at  once  light  in  weight  as  well  as  strong,  dur- 
able and  elastic.  It  is  thoroughly  acid  and  alkali  proof,  is  not  affected 
by  coal  gas  or  smoke  and  can  be  laid  on  either  pitched  or  flat  roofs, 
proving  equally  effectual  in  both  cases.  Inasmuch  as  it  contains  no  tar 
or  asphalt  the  roofing  is  not  affected  by  extremes  in  temperature." 

Ruberoid  is  made  ^-ply  weighing  22  pounds  per  square;  i-ply 
weighing  30  pounds  per  square ;  2-ply  weighing  43  pounds  per  square ; 
and  3-ply  weighing  51  pounds  per  square.  The  2-ply  and  the  3-ply 
roofing  are  commonly  used  for  factories  and  mills.  The  roofing  is  put 
up  in  rolls  36  inches  wide,  containing  two  squares  (200  square  feet), 
with  an  additional  allowance  of  16  square  feet  for  two-inch  laps  at  the 
seams ;  sufficient  tacks,  tin  caps  and  cement  are  included  with  e'ach  roll. 

Ruberoid  roofing  costs  from  $2.75  to  $3.75  per  square  laid  on  the 
roof. 

Ferroinclave. — This  is  a  patented  roofing  made  by  the  Brown 
Hoisting  Machinery  Co.,  Cleveland,  Ohio,  and  is  described  in  a  letter 
to  the  author  as  follows :  "Ferroinclave  roofing  is  made  by  coating  a 
special  crimped  or  corrugated  iron  or  steel  on  both  sides  with  a  mixture 
of  Portland  cement  and  sand,  after  which  it  is  painted  on  the  upper 
side.  The  sheets  are  made  of  No.  22  or  No.  24  sheet  steel,  and  full 
sized  sheets  are  20  inches  wide  and  10  feet  long.  The  steel  is  crimped 
or  corrugated  with  corrugations  about  2  inches  wide  and  ^>  inch  deep, 
the  width  of  the  corrugation  on  the  outer  side  being  less  than  on  the 
inner  side,  thus  forming  a  key  to  hold  the  cement  mortar  in  place.  The 
sheets  are  laid  in  the  same  manner  as  corrugated  steel,  and  a  coating 
of  Portland  cement  mortar,  composed  of  I  part  Portland  cement  and 
2  parts  sand,  is  plastered  on  the  upper  and  lower  surfaces  to  a  thick- 
ness of  Y%  of  an  inch  above  and  below  the  corrugations,  making  the 
total  thickness  of  the  roofing  ij^  inches.  The  weight  of  No.  24  sheet 
steel  Ferroinclave  is  about  15  Ibs.  per  square  foot  when  filled  with  cem- 
ent mortar  as  above.  A  test  of  a  sheet  of  Ferroinclave  made  as  above, 
showed  failure  with  a  uniformly  distributed  load  of  300  Ibs.  per  square 
foot  with  supports  4'  10"  apart,  the  cement  having  set  ten  days.  The 


EXAMPLES  OF  ROOFS  261 

cost  of  this  roofing  is  about  $21 .00  per  square  complete  in  place  on  the 
roof."  The  Brown  Hoisting  Machinery  Co.  has  also  used  Ferroinclave 
quite  extensively  for  floors  and  side  walls  of  buildings. 

Examples  of  Roofs. — The  Boston  Manufacturer's  Mutual  Fire 
Insurance  Co.,  recommend  the  following  roof  for  mill  buildings :  "Roofs 
of  ordinary  type  may  be  only  of  plank  covered  with  composition  or 
other  suitable  roofing  material.  In  special  cases  the  roof  should  consist 
of  a  3-inch  plank,  I  inch  of  mortar,  a  i-inch  top  board  and  a  5~ply  com- 
position roof.  Such  a  roof  is  impervious  to  heat  and  cold." 

The  roof  of  the  machine  shop  of  the  Chicago  City  Railway  is  com- 
posed of  2  x  6-in.  tongued  and  grooved  sheathing  overlaid  with  5  layers 
of  ''Cincinnati"  wool  felt,  having  100  pounds  of  cement  to  100  square 
feet,  and  is  covered  with  tar  and  gravel. 

The  roof  of  the  Lehigh  Valley  R.  R.  Shops  at  Sayre,  Pa.,  is  a  slag 
roofing  on  armored  concrete. 

The  roof  of  the  Great  Northern  R.  R.  shops  at  St.  Paul,  Minn., 
has  double  sheathing  with  I  x  3-in.  strips  between  the  layers  to  provide 
an  air  pace  and  prevent  sweating.  Monarch  roofing  is  laid  on  the 

sheathing. 

The  roof  of  the  Philadelphia  &  Reading  shops,  at  Reading,  Pa., 
is  felt  on  plank  sheathing  covered  with  tar  and  slag. 

The  roof  of  the  A.  T.  &  S.  F.  R.  R.  machine  shops  at  Topeka, 
Kas.,  is  Ludowici  tile  laid  on  2  x  2-in.  timber  strips. 

The  roof  of  the  Union  Train  Shed  at  Peoria,  111.,  is  Ludowici  tile 
laid  on  angle  sub-purlins  as  shown  in  Fig.  87. 

Roof  Coverings  for  Railway  Buildings. — The  following  abstract 
of  the  report  of  the  committee  on  roof  coverings  presented  at  the  an- 
nual meeting  of  the  Association  of  Railway  Superintendents  of  Bridges 
and  Buildings,  1902,  will  give  a  very  good  idea  of  the  present  practice 
in  covering  railroad  buildings. 

"Slate  is  much  used  for  station  buildings  where  there  is  not  much 
climbing  for  repair  of  skylights  or  telegraph  wires.  It  has  a  life  of 
from  35  to  40  years,  and  the  roof  should  have  a  pitch  of  not  less  than 
6  inches  per  foot.  Vitrified  tile  is  very  durable  where  rightly  made 
and  laid  on  steep  roofs,  but  is  not  adapted  for  ordinary  railroad  build- 
ings. Shingle  roofs  last  as  long  as  28  years,  and  should  be  laid  with 


262  ROOF  COVERINGS 

6  inches  pitch  per  foot;  they  are  very  satisfactory  where  slate  is  too 
expensive.  For  flat  roofs  a  tar  and  gravel  composition  is  preferred  and 
will  last  12  to  18,  and  even  20  years.  Slag  or  broken  stone  of  the 
size  of  peas  is  sometimes  used  in  the  place  of  gravel.  In  such  roofs, 
much  depends  upon  the  paper  used,  the  pitch,  and  the  thoroughness  of 
the  work ;  3-ply  is  too  light,  4-ply  is  good,  but  5-ply  is  better.  Asphalt 
pitch  is  sometimes  preferred  to  coal-tar,  but  the  latter  is  sufficiently  dur- 
able. An  asphalt-gravel  roof  must  slope  not  more  than  ^2  inch  to  the 
foot,  on  account  of  the  liability  to  run  in  hot  weather;  but  tar-gravel 
roofs  may  have  a  pitch  of  I  inch  per  foot.  With  such  very  flat  roofs 
as  are  required  for  asphalt,  any  settlement  will  form  hollows  that  will 
hold  water. 

"Sheet  metal  roofs,  corrugated  or  flat  are  not  durable.  Steel  is  less 
durable  than  iron  and  will  last  only  about  one  year,  where  exposed  to 
engine  gases.  Tin  shingles  of  good  quality  give  good  results.  Painted 
shingles  have  a  short  life  unless  frequently  painted. 

"Of  patented  roof  coverings,  Sparham  is  pulverized  talcose  lime 
rock,  mixed  with  coal-tar  pitch  and  applied  hot  to  the  roof  with  a 
trowel.  This  may  be  used  for  a  flat  roof  or  for  a  roof  with  a  pitch  of 
3  or  4  inches  per  foot.  Ruberoid  is  a  wool  felt  saturated  with  a  parafine 
preparation.  %  Perfected  Granite  Roofing  is  2-ply  tarred  paper  with  sea 
grit  on  one  side.  Both  of  these  last  may  be  used  on  any  roof  with  a 
pitch  of  not  less  than  2  inches  per  foot.  Cheap  roofs  made  from  roofing 
papers  require  mopping  with  tar,  and  if  thus  treated  every  two  years 
(before  the  paper  is  bare)  will  last  almost  indefinitely.  In  railway 
work,  however,  roofs  are  generally  left  without  attention  until  leaks 
are  reported,  when  it  is  too  late  for  mopping  to  do  any  good. 

"Roofs  requiring  treatment  every  two  years  can  hardly  be  consid- 
ered as  permanent.  Slate  for  pitched  roofs  and  tar  and  gravel  for  flat 
roofs  are  as  nearly  permanent  as  can  be  obtained  for  railway  buildings. 

"The  cost  per  square  of  100  square  feet  for  roofs  of  different  kinds 
in  New  England  is  as  follows : 

Slate $  9.00  to  $12.00  Tar  and  gravel $4.00  to  $5.00 

Tile 30.00  to     33.00  Sparham 5.00  to     5.50 

Shingles  Ruberoid    2.75  to     3.75 

Sawed  cedar. . .     4.50  to      5.00  Prefected  Granite..  2.75  to    3.25 

Tinned 5.00  to      6.50  Paroid ,.  3.00  to     3.50 

Sheet  tin,  standing  2-pty  double...  2.00  to     2.25 

seam 6.50    to    8.00          3-ply  single  ..   1.50  to  2.00" 


CHAPTER  XX. 
SIDE  WALLS  AND  CONCRETE  BUILDINGS. 

SIDE  WALLS.— The  sides  of  steel  frame  mill  buildings  are  cov- 
ered with  corrugated  steel,  expanded  metal  and  plaster,  wire  lath  and 
plaster,  or  with  Ferroinclave  a  patent  covering  made  of  special  corrug- 
ated steel  and  plaster,  manufactured  by  the  Brown  Hoisting  Co.,  Cleve- 
land, Ohio. 

Corrugated  Steel. — The  methods  of  fastening  corrugated  steel  to 
the  sides  of  buildings  are  the  same  as  on  the  roof  and  are  described 
in  detail  in  Chapter  XVIII.  Where  warmth  is  desired,  buildings  cov- 
ered with  corrugated  steel  are  often  lined  with  No.  26  corrugated  steel 
with  1*4 -inch  corrugations  .  Where  this  lining  is  used  spiking  pieces 
should  be  bolted  to  the  girts  and  intermediate  spiking  pieces  should  be 
placed  between  the  girts  to  which  to  nail  the  lining.  If  this  is  not  done 
the  corrugated  steel  will  gape  open  for  the  reason  that  it  is  impossible 
to  rivet  the  side  laps  of  the  lining.  Where  anti-condensation  lining  is 
used  on  the  sides  it  is  made  the  same  as  on  the  roof  except  that  the 
girts  should  always  be  placed  not  more  than  one-half  the  usual  distance. 
The  clinch-nail  fastening  is  the  best  method  for  fastening  the  corrug- 
ated steel  where  the  anti-condensation  lining  is  used. 

Expanded  Metal  and  Plaster. — The  methods  of  making  walls  of 
expanded  metal  and  plaster  are  shown  in  Fig.  131  and  Fig.  132,  which 
show  details  of  the  construction  of  the  soap  factory  buildings  of  W.  H. 
Walker,  Pittsburg,  Pa.  These  buildings  were  constructed  as  follows: 
The  buildings  were  made  with  a  self-supporting  steel  frame,  all  con- 
nections except  those  for  the  purlins  and  girts  being  riveted.  Inacces- 
sible surfaces  were  painted  with  red  lead  and  linseed  oil  before  erection 
and  the  entire  framework  was  painted  two  coats  of  graphite  paint  after 


264 


SIDE;  WALLS  AND  CONCRETE;  BUILDINGS 


erection.  The  trusses  are  spaced  from  14  to  18  feet  and  carry  6,  7  and 
8-inch  channel  purlins.  The  purlins  are  spaced  from  6  to  7  feet  apart 
and  carry  roof  slabs  25^  to  3  inches  thick  made  of  expanded  metal  and 
concrete.  The  expanded  metal  is  made  from  No.  16  B.  W.  G.  steel 
plate  with  4-inch  mesh,  and  the  concrete  is  composed  of  I  part  Port- 
land cement,  2  parts  sand  and  4  parts  screened  furnace  cinders.  The 
roof  slabs  are  covered  with  10  x  1 2-inch  slate  nailed  directly  to  the 


Slate  - 
±" 

ZT  Concrete- 

Expanded 
Metal" 


Pitch  =i 


Plaster 

Expanded 
Metal   " 


<  Plaster 

Expanded 
"Metal 


Plaster 
Expanded 
"  Metal 

Channel 

"v  Iron 


-Plaster 
'^Channel 
k  Iron  Stud 
I8"l  Beam 


Section  Plan 

through  of 

Head          Window  Box 


Plan 

at 
Column 


Stone  18x18*12" 
Brick 
Concrete 


Grade-' 


k 37' 6" 

FIG.  131.    CROSS-SECTION  OF  STEEL  BUILDING  COVERED  WITH  EXPANDED 

METAL  AND  PLASTER. 

concrete,  and  are  plastered  smooth  on  the  under  side.  The  side  walls 
were  made  by  fastening  24 -inch  channels  at  1 2-inch  centers  to  the  steel 
framing,  and  covering  this  framework  with  expanded  metal  wired  on. 
The  expanded  metal  was  then  covered  on  the  outside  with  a  coating  of 
cement  mortar  composed  of  I  part  Portland  cement  and  2  parts  sand 
and  on  the  inside  with  a  gypsum  plaster,  making  a  wall  about  2  inches 
thick.  The  ground  floors  were  made  by  covering  the  surface  with  a 
6-inch  layer  of  cinders  in  which  were  imbedded  2  x  4-in.  white  pine  nail- 


EXPANDED  METAL  AND  PLASTER 


265 


ing  strips  16  inches  apart,  and  on  these  strips  was  laid  a  floor  of 
tongued  and  grooved  maple  boards  i%  inches  thick  and  2l/2  inches 
wide.  The  upper  floors  are  made  of  concrete  slabs  reinforced  with  ex- 
panded metal,  and  supported  on  beams  spaced  4  to  15  feet  apart.  Where 
the  spans  exceed  7  feet  suspension  bars  7"  x  y%"  were  placed  3  feet 
apart  and  were  bent  around  the  flanges  of  the  beams.  The  concrete 
filling  was  composed  of  I  part  Portland  cement,  2  parts  sand  and  6 
parts  cinders.  (For  another  description  of  this  building  see  Engineer- 
ing Record,  August  25,  1900.) 

-7"  I  Beom 


II 

,-  7 

"I  Beam 

1 

»-7'I  Beom 


,-7"  I  Beom 


6"-, 


I"C  I 


a-;e- 
+  I 

-M  "<0    ' 


h 


FIG.  132.  SIDE  ELEVATION  OF  STEEL  BUILDING  COVERED  WITH  EX- 
PANDED METAL  AND  PLASTER. 

The  Northwestern  Expanded  Metal  Co.  now  recommends  that  the 
first  coat  of  the  plaster  used  for  curtain  walls  be  composed  of  two  parts 
lime  paste,  I  part  Portland  cement  and  3  parts  sand,  and  that  the  wall 
be  finished  with  a  smooth  coat  composed  of  I  part  Portland  cement  and 
2  parts  sand. 

For  coating  on  wire  lath  the  following  has  been  found  to  give 
satisfactory  results  in  Chicago  and  vicinity:  For  the  first  coat  use  a 


266  SIDE  WALLS  AND  CONCRETE  BUILDINGS 

mortar  composed  of  I  part  Portland  cement  and  2  parts  ordinary  lime 
mortar.  The  lime  should  be  very  thoroughly  slaked  before  using  as 
the  presence  of  any  free  lime  will  injure  the  wall.  After  the  first  coat 
has  hardened  it  is  thoroughly  soaked  and  a  finishing  coat  composed  of 

1  part  Portland  cement,  2  parts  sand  and  a  small  quantity  of  slaked 
lime  is  applied  and  rubbed  smooth. 

A  method  of  plastering  curtain  walls  is  described  by  Mr.  George 
Hill  in  the  Transactions  of  the  American  Society  of  Civil  Engineers, 
Vol.  29,  as  follows :  "The  external  curtain  walls  were  composed  of  hard 
plaster,  Portland  cement  and  sand  in  equal  parts,  the  scratch  coat  being 
applied  to  uncoated  metallic  lath,  making  the  thickness  of  the  scratch 
coat  about  I  inch ;  then  a  surfacing  of  Portland  cement  j^-inch  thick 
was  applied  on  each  side  making  the  curtain  walls  a  total  thickness  of 

2  inches.    Good  results  were  obtained  in  every  case  except  one,  where 
the  scratch  coat  was  alternately  frozen  and  thawed  several  times,  and 
the  outer  surfacing  of  the  wall  peeled  off  in  patches/' 

The  Northwestern  Expanded  Metal  Co.  does  not  recommend  the 
use  of  hard  or  patent  plasters  for  curtain  walls. 

Expanded  metal  and  plaster  curtain  walls  are  light,  strong  and 
efficient.  They  do  not  require  the  heavy  foundations  required  by  brick 
and  stone  walls  and  are  fireproof.  They  can  be  used  to  advantage 
where  it  is  desirable  to  have  a  large  glass  area  in  the  sides  of  buildings. 
This  type  of  construction  is  almost  ideal  for  factory  construction  and 
will  be  much  used  in  the  future.  There  are  quite  a  number  of  different 
systems  but  the  methods  of  construction  are  essentially  the  same  in  all. 

Curtain  walls  are  made  of  wire  lath  and  plaster  in  the  same  way 
as  expanded  metal  and  plaster  and  have  all  the  advantages  of  the  latter. 

The  cost  of  curtain  walls  made  as  described  above  is  about  $1.50 
to  $1.80  per  square  yard. 

For  a  detailed  description  of  the  construction  of  small  cement  and 
steel  buildings  see  Engineering  Record,  March  26,  1898. 

Concrete  Slabs. — The  construction  of  reinforced  concrete  slabs 
patented  by  Milliken  Brothers,  New  York,  is  described  in  Engineering 


MASONRY  WALLS  267 

Record,  December  22,  1900,  as  follows :  "The  slabs  used  on  the  roof 
of  the  concrete  stable  built  for  the  Anglo- Swiss  Condensed  Milk  Com- 
pany, Brooklyn,  N.  Y.,  were  4  feet  wide  and  about  15  feet  long  and 
were  constructed  as  follows:  Each  slab  has  a  steel  frame  with  three 
2  x  54 -inch  transverse  strips  set  edgewise  at  the  ends  and  middle,  and 
connected  by  longitudinal  ^4 -inch  rods  about  3^  inches  apart  so  as  to 
form  a  gridiron.  The  rods  are  set  in  staggered  holes  in  the  edge  of 
the  bars  and  form  a  framework  over  and  under  which  No.  14  trans- 
verse wires  are  woven  6  inches  apart.  The  lower  surface  of  the  frame 
is  covered  with  open  mesh  fine-wire  netting,  wired  around  the  edges, 
and  the  frame  is  filled  with  1:2:4  Portland  cement  concrete  made  with 
very  fine  broken  stone.  The  slab  is  2  inches  thick  and  has  offset  edges 
to  make  scarfed  joints  which  are  set  with  cement  mortar.  Voids  are 
left  in  the  concrete  at  the  edges  of  the  slabs  to  permit  thin  flat  steel 
bars  or  angle  clips  to  be  bolted  to  the  frames,  and  to  be  bolted  to  or 
locked  around  the  framework.  Then  the  holes  are  flushed  with  cement 
mortar  and  a  J^-inch  surface  coat  is  plastered  over  the  slabs  for  the 
final  finish.  These  slabs  have  been  used  for  side  and  partition  walls 
as  well  as  for  roof  sheathing." 

Masonry  Walls. — Walls  for  filling  in  between  the  columns  of 
mill  buildings  are  commonly  made  very  light,  being  usually  determined 
by  the  clearance  and  the  height.  For  buildings  with  20  to  25  ft.  posts, 
8-inch  walls  are  very  commonly  used.  Where  the  columns  are  placed 
inside  of  the  line  of  the  walls,  a  greater  thickness  of  wall  is  used  than 
above;  13  and  1 7-inch  walls  being  quite  common. 

The  thickness  of  factory  and  warehouse  walls  which  support  roof 
trusses  is  about  as  given  in  Table  XXII. 

The  thickness  of  the  wall  may  be  decreased  when  pilasters  are  used 
to  assist  in  supporting  the  trusses. 

For  detailed  information  on  the  construction  of  brick  and  stone 
walls  see  Baker's  Masonry  Construction  and  Kidder's  Building  Con- 
struction and  Superintendence,  Part  I. 

'9 


268  SIDE  WALLS  AND  CONCRETE  BUILDINGS 

TABLE  XXII. 
THICKNESS  OF  WAREHOUSE  WALLS. 


Height 
of 
Wall. 
Feet. 

Thickness  of  Wall. 

Brick. 
Inches. 

Stone. 
Inches. 

25 
50 
75 

16 
20 
24 

20 
24 
36 

CONCRETE  BUILDINGS.— Within  the  last  few  years  quite  a 
number  of  factory  buildings  have  been  constructed  of  concrete.  Most 
of  these  buildings  are  monolithic,  although  recently  quite  a  number  of 
patents  have  been  issued  for  concrete  building  blocks.  The  walls  are 
usually  made  hollow  wrien  made  monolithic  or  made  of  concrete  blocks ; 
the  air  space  prevents  the  passage  of  dampness  through  the  walls,  makes 
the  building  warmer  and  is  less  expensive  than  to  make  the  wall  solid. 
In  monolithic  concrete  construction  the  roof,  floors  and  the  angles  in 
the  walls  are  reinforced  with  metal  put  in  according  to  some  one  of  the 
many  systems  now  in  use. 

The  following  abstract  of  the  description  of  the  construction  of  a 
monolithic  concrete  building,  printed  in  the  Engineering  Record,  July 
3Oth,  and  August  2Oth.,  1898,  will  give  the  reader  an  idea  of  the 
methods  employed. 

"The  factory  of  the  Pacific  Coast  Borax  Company,  at  Constable 
Hook,  Bayonne,  N.  J.,  is  about  200  x  250  feet  in  extreme  dimensions, 
and  is  partly  one  story  and  partly  four  stories  in  height.  All  the  floors, 
floor  beams,  walls,  columns,  etc.  are  constructed  of  reinforced  concrete 
on  the  Ransome  system,  built  in  molds  so  as  to  form  a  monolithic  struc- 
ture continuous  throughout,  except  for  the  shrinkage  joints  dividing 
it  into  separate  panels. 

"The  columns  are  supported  on  concrete  footings  reinforced  with 
twisted  steel  bars.  The  walls  of  the  building  were  built  solid  at  the 
ends  of  the  floor  beams  and  the  intermediate  portions  were  made  hoi 


CONCRETE:  BUILDINGS  269 

low  by  inserting  wooden  fillers,  which  were  afterwards  removed.  The 
walls  of  the  four  story  portion  are  16  inches  in  extreme  thickness  up  to 
the  third  floor,  and  are  15  inches  above  that  point.  The  hollow  walls 
have  3  to  4  inches  of  concrete  on  each  side  of  the  air  space.  Both  the 
walls  and  the  columns  were  bonded  by  vertical  bars  of  twisted  steel  24- 
inch  square,  extending  through  them  continuously  from  top  to  bottom, 
and  similar  rods  were  carried  through  the  buildings  from  side  to  side 
transverse  to  .the  beams  imbedded  in  the  different  floors  about  12  feet, 
apart  so  as  to  provide  a  certain  transmission  of  the  strain  across  the 
building  and  assure  the  resistance  of  the  structure  as  a  whole  under  the 
action  of  eccentric  loads  and  pressures. 

"At  about  every  25  feet  in  the  length  of  the  walls  a  vertical  space 
of  %  of  an  inch  was  made,  extending  from  top  to  bottom  and  separat- 
ing the  wall  into  distinct  sections.  At  each  of  these  joints  a  twisted 
24 -inch  rod  was  imbedded  from  top  to  bottom  on  each  side  of  the  space. 
Similar  rods  were  also  placed  at  the  corners  of  the  building.  Where 
the  vertical  shrinkage  joints  occur  in  the  outside  walls  the  continuity 
of  the  structure  is  preserved  by  carrying  through  them  horizontal  lon- 
gitudinal pieces  of  twisted  ^-inch  square  rods  about  2  teet  long  and 
set  about  2  feet  apart  throughout  the  height  of  the  wall. 

"The  columns  were  built  in  1 6- foot  sections,  each  section  being  one 
story  in  height,  and  were  constructed  by  ramming  the  concrete  inside 
of  forms.  The  vertical  boards  composing  these  forms  were  made  in 
short  lengths,  breaking  joints  over  the  cross  pieces,  and  were  placed 
in  position  as  the  concrete  was  placed  in  position.  The  forms  were  al- 
lowed to  stand  until  required  for  another  story,  often  remaining  in  po- 
sition for  several  weeks,  although  it  was  considered  that  the  concrete 
was  strong  enough  to  permit  their  removal  when  48  hours  old.  The 
walls  were  laid  up  between  vertical  surfaces  of  plain  i^-inch  plank, 
laid  horizontally  and  secured  by  tie  bolts  running  through  the  molds. 
The  wall  was  built  up  in  sections  about  four  feet  in  height  and 
the  concrete  was  laid  in  continuous  6-inch  layers,  extending  en- 
tirely around  the  circumference  of  the  wall,  and  was  thoroughly 
rammed  as  deposited.  After  the  concrete  had  set  sufficiently,  the  bolts 
were  loosened  and  the  boards  forming  the  sides  of  the  mold  were  pulled 
up  and  set  in  position  for  building  another  zone  of  wall.  About  35 
men  were  at  work  building  the  walls  and  constructed  an  average  of 
2000  square  feet  a  day. 


270  SIDE  WALLS  AND  CONCRETE  BUILDINGS 

"The  partitions  in  the  building  are  2  inches  thick  and  are  made  of 
solid  concrete  reinforced  by  a  framework  of  twisted  ^4 -inch  bars  about 
2  feet  apart,  both  vertically  and  horizontally.  The  partitions  were  built 
in  molds,  and  set  so  that  the  face  comes  exactly  even  with  the  edge 
of  a  shrinkage  joint  in  the  floor,  and  always  set  over  a  floor  beam. 

"The  concrete  was  made  of  Atlas  cement  and  broken  basaltic  rock, 
all  of  which  will  pass  through  a  2-inch  ring  and  most  of  which  will 
pass  through  a  i-inch  ring.  The  unscreened  rock  was  mixed  with 
cement  in  the  following  proportions:  For  foundations,  I  to  10;  for  the 
walls,  floors  and  most  of  the  work,  I  to  6^  ;  for  the  columns,  I  to  5 ; 
and  for  the  lower  chords  of  the  floor  beams,  I  to  6,  using  very  fine 
stone." 

In  constructing  the  Ingalls  office  building  in  Cincinnati,  Ohio,— • 
described  in  Engineering  News,  July  30,  1903,  and  Engineering  Record, 
July  1 8,  1903 — the  methods  used  were  essentially  the  same  as  de- 
scribed above  with  a  few  exceptions  which  will  be  noted. 

"The  broken  stone  included  the  total  product  of  the  crusher  and  was 
fine  enough  to  pass  through  a  i-inch  screen.  The  concrete  was  mixed 
rather  wet  to  insure  complete  filling  of  all  interstices  around  the  bars. 
Enough  water  was  used  to  always  give  a  semi-fluid  consistency  which 
allowed  puddling  rather  than  ramming.  It  was  made  wetter  for  the 
columns  than  for  the  floors  and  girders  because  the  bars  interferred 
with  the  ramming  in  the  molds  for  the  columns.  The  columns  were 
built  in  one-story  lengths  and  the  concrete  was  rammed  in  the  molds  in 
layers  not  more  than  12  inches  deep.  The  concrete  was  dumped  from 
the  floor  above  into  the  bottom  of  the  mold.  The  steel  rods  were 
placed  in  position  before  the  concreting  was  commenced,  and  were 
wired  in  position.  A  force  of  28  men  working  with  hoisting  machines 
and  wheelbarrows  placed  about  100  cubic  yards  of  concrete  in  a  day.*' 

The  present  tendency  in  concrete  building  construction  is  toward 
the  use  of  a  concrete  made  of  Portland  cement  and  finely  crushed  stone, 
mixed  very  wet  and  deposited  in  the  molds  practically  without  ram- 
ming. The  concrete  must  be  rich  in  cement  to  make  a  good  wall  ur.« 
der  these  conditions. 


CONCRETE  BUILDINGS  271 

Surface  Finish. — Where  it  is  desired  to  imitate  stonework,  imita- 
tion Joints  are  formed  in  the  face  of  the  wall  and  the  surface  is  either 
picked  while  the  concrete  is  yet  tender  or  is  tooled  after  the  concrete 
has  hardened.  Bush  hammering  of  concrete  walls  can  be  done  by  an 
ordinary  workman  for  from  iy2  to  2  cts.  per  sq.  ft.  Where  the  con- 
crete is  coarse  a  coating  of  cement  mortar  may  be  applied  as  the  con- 
crete is  placed  in  the  molds  by  means  of  a  piece  of  sheet  steel  placed 
from  I  to  2  inches  from  the  forms;  the  cement  mortar,  usually  made 
of  I  part  Portland  cement  and  2  parts  sand,  is  then  rammed  into  the 
vacant  space,  after  the  main  body  of  the  concrete  has  been  rammed  in 
place,  and  the  piece  of  sheet  steel  is  removed. 

The  preparation  of  the  forms  requires  considerable  study  to  obtain 
a  smooth  surface  and  unbroken  corners.  The  use  of  matched  or 
tongued-and-grooved  stuff  is  not  desirable  as  the  concrete  fills  the  open- 
ings made  by  shrinkage  and  there  is  no  room  to  expand.  Unmatched 
boards  dry  apart  and  let  the  water  in  the  concrete  leak  out,  carrying 
with  it  some  of  the  cement.  The  best  way  to  build  the  forms  is  to  use 
narrow  stuff  and  bevel  one  edge  of  the  boards ;  the  sharp  edge  of  the 
bevel  lying  against  the  square  edge  of  the  adjoining  board  allows  the 
edge  to  crush  when  swelling  and  closes  up  the  joint.  A  coat  of  soft 
soap  applied  to  the  forms  before  filling,  prevents  the  concrete  from  ad- 
hering. The  soap  should  be  scraped  and  brushed  off  with  a  steel 
brush  as  the  forms  are  removed. 

For  description  of  concrete  round  house  at  Moose  Jaw,  Canada, 
see  Part  IV. 


CHAPTER  XXI. 
FOUNDATIONS. 

Introduction. — The  design  of  the  foundations  for  mill  buildings 
is  ordinarily  a  simple  matter  for  the  reason  that  the  buildings  are  usu- 
ally located  on  solid  ground  and  the  loads  on  the  columns  are  small. 
Where  the  soil  is  treacherous  or  when  an  attempt  is  made  to  fix  the 
columns  at  the  base  the  problem  may,  however,  become  quite  com- 
plicated. 

Bearing  Power  of  Soils. — The  bearing  power  of  a  soil  depends 
upon  the  character  of  the  soil,  its  freedom  from  water,  and  its  lateral 
support.  The  downward  pressure  of  the  surrounding  soil  prevents  lat- 
eral displacement  of  the  material  under  the  foundation  and  adds  ma- 
terially to  the  bearing  power  of  treacherous  soils. 

The  safe  bearing  power  of  soils  given  in  Table  XXIII  may  be 
used  as  an  aid  to  the  judgment  in  determining  on  a  safe  load  for  a 
foundation.  However  no  important  foundations  should  be  built  with- 
out making  careful  soundings  and  bearing  tests. 

A  soil  incapable  of  supporting  the  required  loads  may  have  its 
supporting  power  increased  (i)  by  increasing  the  depth  of  the  foun- 
dation; (2)  by  draining  the  site;  (3)  by  compacting  the  soil;  (4)  by 
adding  a  layer  of  sand  or  gravel;  (5)  by  using  timber  grillage  to  in- 
crease the  bearing  area ;  (6)  by  driving  piles  through  the  soft  stratum, 
or  far  enough  into  it  to  support  the  loads. 

A  method  used  in  France  for  compacting  foundations  is  to  drive 
holes  with  a  heavy  metal  plunger  and  then  fill  these  holes  with  closely 
rammed  sand  or  gravel. 

Several  kinds  of  patented  concrete  piles  are  now  in  use  to  a  limited 
extent  in  this  country  for  building  foundations. 


BEARING  POWER  OF  SOILS 


273 


TABLE  XXIII. 
SAFE  BEARING  POWER  OF  SOILS.* 


TTind   nf   Material 

Safe  Bearing 
per  S 

Power  in  Tons 
q.  Ft. 

Min. 

Max. 

Bock-hardest  in  thick  layers  in  bed.  .  .  . 
"      equal  to  best  ashlar  masonry.  .  .  . 
"         "      "      "      brick  

200 
25 
15 

30 

20 

"         "          poor  brick  

5 

10 

Clay  in  thick  beds,  always  dry  

4 

6 

«•     i4       "       "  moderately  dry  

2 

4 

•'     soft  

1 

2 

Gravel  and  coarse  sand,  well  cemented 
Sand  compact  and  well  cemented 

8 
4 

10 
6 

"    clean,  dry  

2 

4 

Quicksand,  alluvial  soils,  etc  

0.5 

1 

When  foundations  are  placed  on  solid  rock,  the  surface  of  the 
rock  should  be  carefully  cleaned  of  loose  and  rotten  rock  and  roughly 
brought  to  a  surface  as  nearly  perpendicular  to  the  direction  of  the 
pressure  as  practicable.  A  layer  of  cement  mortar  placed  directly  on 
the  rock  surface  will  assist  in  bonding  the  foundations  and  the  footing 
together. 

When  foundations  are  placed  on  sand,  gravel  or  clay  it  is  usually 
only  necessary  to  dig  a  trench  and  start  the  foundation  below  frost.  If 
the  soil  is  somewhat  yielding  or  if  the  load  is  heavy  the  foundation 
should  be  carried  to  a  greater  depth  or  the  footings  should  be  made 
wider  than  for  greater  depths. 

Bearing  Power  of  Piles. — Probably  no  subject  has  been  more 
freely  discussed  and  with  more  conflicting  views  and  opinions  than  has 
the  safe  bearing  power  of  piles.  The  safe  load  to  put  on  a  pile  in  any  par- 
ticular case  is  dependent  upon  so  many  conditions  that  any  formula  for 
the  safe  bearing  power  is  necessarily  simply  an  aid  to  the  judgment 
of  the  engineer,  and  not  an  infallible  rule  to  be  blindly  followed.  All 


*Treatise  on  Masonry  Construction,  by   Ira   0.    Baker,— John   Wiley   &   SOQS, 
Publishers,    New    York. 


274  FOUNDATIONS 

formulas  for  the  bearing  power  of  piles  determine  the  safe  bearing 
power  from  the  weight  of  the  hammer,  the  length  of  free  fall  of  the 
hammer,  and  the  penetration  of  the  pile.  The  penetration  of  the  pile 
for  any  blow  of  the  hammer  depends  on  the  condition  of  the  head  of 
the  pile,  upon  whether  the  pile  is  driving  straight,  and  upon  the 
rigidity  of  the  pile.  The  penetration  of  a  slim,  limber  pile  with  a 
broomed  head  is  very  misleading,  and  any  formula  will  give  values  too 
large. 

The  Engineering  News  formula  for  the  safe  bearing  power  of 
piles  is  most  used  and  is  certainly  the  most  reliable.    It  is 


where  P  =  safe  load  on  pile  in  tons; 

W  =  weight  of  hammer  in  tons  ; 

h  =  distance  of  free  fall  of  the  hammer  in  feet  ; 

s  =    penetration  of  the  pile  for  the  last  blow  in  inches. 

If  the  pile  is  driven  with  a  steam  hammer  the  factor  unity  in  the 
denominator  is  changed  to  one-tenth.  This  formula  is  supposed  to  give 
a  factor  of  safety  of  about  6,  and  has  been  shown  by  actual  use  to  give 
values  that  are  safe. 

Where  piles  are  to  be  driven  through  gravel  or  very  hard  ground 
the  lower  ends  are  often  protected  with  cast  iron  or  steel  points.  The 
value  of  these  points  is  questionable  and  most  engineers  now  prefer  to 
drive  piles  without  their  use,  simply  making  a  very  blunt  point  on  the 
pile.  In  driving  piles,  care  must  be  used  where  small  penetrations  are 
obtained  not  to  smash  or  shiver  the  pile.  Piles  driven  to  a  good  refusal 
with  a  penetration  of,  say,  I  inch  for  the  last  blow,  with  a  fall  of  20  ft. 
and  a  2OOO-lb.  hammer  will  safely  support  almost  any  load  that  can  be 
put  on  them. 

Piles  are  usually  driven  at  about  3-ft.  centers  over  the  bottom  of 
the  foundation.  After  the  piles  are  driven  they  are  sawed  off  below  the 
water  level  and  (  I  )  concrete  is  deposited  around  the  heads  of  the  piles,  or 
(2)  a  grillage  or  platform  is  built  on  top  of  the  piles  to  support  the  walls 


PRESSURE  OF  WALLS  ON  FOUNDATIONS 


275 


or  piers.    The  first  method  is  now  the  most  common  one  for  mill  build- 
ing foundations. 

Pressure  of  Walls  on  Foundations. — In  Fig.  133,  let  W  =  re- 
sultant weight  of  the  wall,  the  footing  and  the  load  on  the  wall, 
/  =  length  of  the  footing  and  b  =  distance  from  center  of  gravity  of 
footing  to  point  of  application  of  load  W,  and  let  the  wall  be  of  unit 


—_^-— 

I 

*• 

i 
j 

1 

—  Vj 

-       N/3 

A 
\A 

W 

4 

W 

0 

£>; 

ff 

II 

I- I d-i 

14, 


FIG.  133. 


FIG.  134. 


length.  The  pressure  on  the  footing  will  be  that  due  to  direct  load 
JV,  and  a  couple  with  an  arm  b  and  a  moment  =  +  Wb.  The  pressure 
due  to  the  direct  W  will  be 

PI  =  W  -r-  /  as  shown  in  (a), 


276  FOUNDATIONS 

and  the  maximum  pressure  due  to  the  bending  moment,  M  =  +  Wb, 
will  be 

p         Me  _6  Wb 
2 7"       ~~7T~ 

The  pressure  at  A  will  be 
and  at  B  will  be 


as  shown  in  (c). 

Now  if  P!  is  made  equal  to  P2  the  pressure  at  B  will  be  zero  and 
at  A  will  be  twice  the  average  pressure.  Placing  P1  =  P2  in  (84)  and 
solving  for  b,  we  have  b  =  %  /.  This  leads  to  the  theory  of  the  middle 
third  or  kern  of  a  section.  If  the  point  of  application  of  the  load  never 
falls  outside  of  the  middle  third  there  will  be  no  tension  in  the  ma- 
sonry or  between  the  masonry  and  foundation,  and  the  maximum  com- 
pression will  never  be  more  than  twice  the  average  shown  in  (a). 

If  the  point  of  application  of  the  load  falls  outside  the  middle  third 
(b  greater  than  %  /)  there  will  be  tension  at  Bf  and  the  compres- 
sion at  A  will  be  more  than  twice  the  average.  But  since  neither  the 
masonry  nor  foundation  can  take  tension,  formulas  (83)  and  (84) 
will  give  erroneous  results. 

In  (d)  Fig.  133,  assume  that  b  is  greater  than  l/(>  /,  and  then  as 
above,  the  load  W  will  pass  through  the  center  of  pressures  which  will 
vary  from  zero  at  the  right  to  P  at  A.  If  3  a  is  the  length  of  the 
foundation  which  is  under  pressure,  then  from  the  fundamental  con- 
dition for  equilibrium  for  translation,  summation  vertical  forces  equals 
zero,  we  will  have 

W  =  y2  P  3  a  and 

(85) 


PRESSURE  OF  PIER  ON  FOUNDATIONS  277 

Pressure  of  a  Pier  on  Foundation.  —  In  Fig.  134,  let  W  =  resul- 
tant of  the  stresses  in  the  column  and  the  weight  of  the  pier,  /  =  length, 
c  =  depth  and  n  =  the  breadth  of  the  footing  of  the  pier  in  feet.  The 
bending  moment  at  the  top  of  the  pier  is  M  =  —  ]/2  H  d  and  at  the  base 
of  the  pier  is  M±  =  —  H  (y£  d  -f-  c).  Now  the  pier  must  be  designed 
so  the  maximum  pressure  on  the  foundation  due  to  W  and  the  bending 
moment  M±  will  not  exceed  the  allowable  pressure.  The  maximum 
pressure  on  the  foundation  will  be 

.  p-/>isb  P*-*L±*L 


W       3  H  (d  -f-  2  c) 

*"  7^  =fc         ^~~  (86) 

It  will  be  seen  from  (86)  that  a  shallow  pier  with  a  long  base  is 
most  economical. 

To  find  the  relations  between  /  and  c  when  the  maximum  pressure 
is  twice  the  average,  place 

W  =  3  H  (d  +  2  c) 
In  n  P 

and  /  -    3/7(^+2,)  (87) 

For  any  given  conditions  the  value  of  /  that  will  be  a  minimum 
may  be  found  by  substituting  in  the  second  member  of  (87)  . 

To  illustrate  the  method  of  calculating  the  size  of  a  pier  we  will 
calculate  the  pier  required  to  fix  the  leeward  column  in  Fig.  57. 

The  sum  of  the  stresses  in  column  ^-17  is  a  minimum  for  dead 
and  wind  load  and  will  be  (Table  V)  equal  to  4800  +  4500  = 
9300  Ibs. 

Try  a  pier  3'  o"  x  3'  o"  on  top,    6'  o"  x  6'  o"    on    the    base 
and  6  feet  deep,  weighing  about  16,700  Ibs. 

Substituting  in  (86)  we  have 

p  =  26,000  ^  3  X  4300  (14  +  12) 

36  6  X  36 

=  722  ±  1553 


278  FOUNDATIONS 

This  gives  tension  on  the  windward  side  which  will  not  do,  and 
so  we  will  reinforce  the  footing  with  beams  and  make  /  =  10  ft.,  and 
increasing  weight  so  that  W  =  40800  Ibs. 

P  =  680  =b  559 

=  1239  or  121  Ibs.  per  square  foot,  which 
is  safe  for  ordinary  soils. 

If  it  had  been  necessary  to  drive  piles  for  this  pier,  a  small  amount 
of  tension  might  have  been  allowed  on  the  windward  side  if  the  tops  of 
the  piles  had  been  enclosed  in  concrete. 

Design  of  Footings. — The  thickness  and  length  of  the  offsets  in 
a  concrete  or  masonry  footing  are  commonly  calculated  as  for  a  beam 
fixed  at  one  end  and  loaded  with  a  uniform  load  over  the  projecting 
part  equal  to  the  maximum  pressure  on  the  footing.  If  p  =  projection 
of  the  footing  in  inches ;  t  =  the  thickness  of  the  footing  in  inches  ;  P  = 
pressure  on  foundation  in  pounds  per  sq.  ft.;  and  S  =  safe  working 
load  of  the  material  of  which  the  footing  is  made  in  pounds  per  square 
inch,  by  substituting  in  the  fundamental  formula  for  flexure  and 
solving  for  pf 

P  "  *  '  4     ¥  (88) 

The  values  of  S  in  common  use  are :  firct  class  Portland  cement 
concrete  50  Ibs.;  ordinary  concrete  30  Ibs.;  limestone  150  Ibs.;  granite 
1 80  Ibs. ;  brickwork  in  cement  50  Ibs. 

The  projection  and  thickness  of  the  footing  course  is  sometimes 
calculated  on  the  assumption  that  the  footing  course  is  a  beam  fixed  at 
the  center,  in  place  of  as  above.  This  solution  hardly  appears  to  be 
justified. 

Pressure  of  Column  on  Masonry. — The  following  pressures  in 
pounds  per  square  inch  are  allowed  by  the  building  laws  of  New 
York. — Portland  cement  concrete  230  Ibs. ;  Rosendale  cement  concrete 
125  Ibs.;  Rubble  stonework  laid  in  Portland  cement  mortar  140  Ibs.; 
brickwork  laid  in  Portland  cement  mortar  250  Ibs. ;  brickwork  laid  in 
lime  mortar  no  Ibs. ;  granite  1000  Ibs. ;  limestone  700  Ibs.  It  is  very  com- 
mon to  specify  250  Ibs.  per  square  inch  for  bearing  on  good  Portland 
cement  pedestals,  and  300  Ibs.  per  square  inch  is  not  uncommon. 


ALLOWABLE  PRESSURES  279 

Allowable  Pressures. — The   following  unit  pressures  have  been 
proposed  by  Mr.  C.  C.  Schneider  in  "  Structural  Design  of  Buildings."  * 

1.  Foundations. — Pressure  on  foundations  not  to  exceed,  in  tons 
per  square  foot: 

Soft  clay I 

Ordinary  clay  and  dry  sand  mixed  with  clay 2 

Dry   sand  and  dry  clay 3 

Hard  clay  and  firm,  coarse  sand 4 

Firm,  coarse  sand  and  gravel 6 

2.  Masonry. — Working  pressure  in  masonry  not  to  exceed,  in 
tons  per  square  foot : 

Common  brick,  Rosendale-cement  mortar 10 

"      Portland-cement  mortar  ; 12 

Hard-burned   brick,    Portland-cement   mortar 15 

Rubble  masonry,  Rosendale-cement  mortar 8 

"              "          Portland-cement  mortar 10 

Coursed  rubble,  Portland-cement  mortar 12 

First-class  masonry,  sandstone 20 

"          "            "          limestone  25 

"          "            "          granite  30 

Concrete  for  walls: 

Portland  cement  1-2-5 2O 

"        1-2-4    25 

3.  Pressure   on    Wall-Plates. — The   pressure   of  beams,   girders, 
wall  plates,  column  bases,  etc.,  on  masonry  shall  not  exceed  the  fol- 
lowing, in  pounds  per  square  inch. 

On  brickwork  with  cement  mortar 200 

"  rubble  masonry  with  cement  mortar 200 

"  Portland-cement  concrete 350 

"  first-class  sandstone  400 

"      "         "    limestone 500 

"      "         "    granite   600 

4.  Bearing  Power  of  Piles. — The  maximum  load  carried  by  any 
pile  shall  not  exceed  40,000  Ibs.,  or  600  Ibs.  per  sq.  in.  of  its  average 
cross-sections. 


*  Trans.  Am.  Soc.  C.  E.,  Vol.  54,  1905. 


2So  FOUNDATIONS 

Piles  driven  in  firm  soil  to  rock  may  be  loaded  to  the  above  limits. 
Piles  driven  through  loose,  wet  soil  to  solid  rock  or  equivalent  bearing 
shall  be  figured  as  columns  with  a  maximum  unit  strain  of  600  Ibs.  per 
sq.  in.,  properly  reduced. 

The  minimum  distance  between  centers  of  piles  shall  be  2.^/2  ft. 

5.  Loads  on  Fdundations. — The  live  loads  on  foundations  shall 
be  assumed  to  be  the  same  as  for  the  footings  of  columns.    The  areas 
of  the  bases  of  the  foundations  shall  be  proportioned  for  the  dead  load 
only.    That  foundation  which  receives  the  largest  ratio  of  live  to  dead 
load  shall  be  selected  and  proportioned  for  the  combined  dead  and 
live  loads.     The  dead  load  on  this  foundation  shall  be  divided  by  the 
area  thus  found,  and  this  reduced  pressure  per  square  foot  shall  be 
the  permissible  working  pressure  to  be  used  for  the  dead  load  of  all 
foundations. 

6.  Reduction  of  Live  Load  on  Columns. — For  columns  carry- 
ing more  than  five  floors,  these  live  loads  may  be  reduced  as  follows : 

For  columns  supporting  the  roof  and  top  floor,  no  reductions; 

For  columns  supporting  each  succeeding  floor,  a  reduction  of 
5  per  cent  of  the  total  live  load  may  be  made  until  50  per 
cent  is  reached,  which  reduced  load  shall  be  used  for  the 
columns  supporting  all  remaining  floors. 


CHAPTER  XXII. 
FLOORS. 

Introduction. — The  requirements  and  the  local  conditions  govern- 
ing the  design  of  floors  for  shops  and  mills  are  so  varied  and  diversified 
that  the  subject  of  floor  design  can  be  treated  only  in  a  general  way. 
Floors  will  be  discussed  under  the  head  of  (i)  ground  floors  and  (2) 
floors  above  ground. 

GROUND  FLOORS.— Types  of  Floors.— There  are  three  gen- 
eral types  of  ground  floors  in  use  in  mills  and  shops:  (i)  solid  heat 
conducting  floors  as  stone,  brick  or  concrete;  (2)  semi-elastic,  semi- 
heat  conducting  floors  as  earth,  macadam  or  asphalt;  (3)  elastic  non- 
heat  conducting  floors  of  wood  or  with  a  wooden  wearing  surface. 

1 i )  Floors  of  the  first  class  have  been  used  in  Europe  and  form- 
erly in  this  country  to  quite  an  extent  in  shops  and  mills,  and  at  pres- 
ent are  much  used  in  round  houses,  smelters,  foundries  and  in  other 
buildings  where  the  wear  and  tear  are  considerable  or  where  men  are 
not  required  to  stand  alongside  a  machine.     Floors  of  this  class  are 
cold  and  damp  and  make  workmen  uncomfortable.    The  wooden  shoes 
of  the  continental  workmen  or  the  wooden  platforms  in  use  in  many  of 
our  shops  which  have  floors  of  this  class,  overcome  the  above  objec- 
tions to  some  extent.    The  gritty  dust  arising  from  most  concrete  floors 
is  very  objectionable  where  delicate  machinery  is  used.    The  noise  and 
danger  from  breakage  and  first  cost  are  additional  objections  to  floors 
of  this  class. 

(2)  Floors  of  this  class  have  many  of  the  objections  and  defects 
of  floors  of  the  first  class.    These  floors  are  liable  to  be  cold  and  damp 
unless  properly  drained,  and  give  rise  to  a  gritty  dust  that  is  often  in- 
tolerable in  a  machine  shop. 


282  FLOORS 

Earth  and  cinder  floors  are  very  cheap  and  are  adapted  to  forge 
shops  and  many  other  places  where  concrete  and  brick  floors  are  now 
put  down.  Floors  of  this  class  should  be  well  tamped  in  layers  and 
should  be  carefully  drained.  Tar-concrete  and  asphalt  floors  are  more 
elastic  and  conduct  less  heat  than  any  of  the  floors  above  mentioned,  but 
the  surface  is  not  sufficiently  stable  to  support  machinery  directly,  and 
floors  of  this  class  are  very  much  improved  by  the  addition  of  a  contin- 
uous wooden  wearing  surface. 

(3)  Floors  of  wood  or  with  a  wooden  wearing  surface  appear  to 
be  the  most  desirable  for  shops,  mills  and  factories.  Wooden  floors  are 
elastic,  non-heat  conducting  and  are  pleasant  to  work  on.  They  are 
cheap,  easily  laid,  repaired  and  renewed.  They  are  easily  kept  clean  and 
do  not  give  rise  to  grit  and  dust. 

The  most  satisfactory  wearing  surface  on  a  wooden  floor  is  rock 
maple  %  to  il/±  inches  thick  and  2^/2  to  4  inches  wide,  matched  or  not 
as  desired.  The  matched  flooring  makes  a  somewhat  smoother  floor  and 
is  on  the  whole  the  most  satisfactory.  The  wearing  floor  should  be 
laid  to  break  joints  and  should  be  nailed  to  planking  or  stringers  laid 
at  right  angles  to  the  surface  layer.  The  thickness  of  the  planking  will 
depend  upon  the  foundation  and  upon  the  use  to  which  the  floor  is  to 
be  put. 

The  different  classes  of  floors  will  now  be  briefly  discussed  and  illus- 
trated by  examples  of  floors  in  use. 

Cement  Floors. — The  construction  of  cement  or  concrete  floors  is 
similar  to  the  construction  of  cement  sidewalks,  the  only  difference 
being  that  the  floor  usually  requires  the  better  foundation.  The  foun- 
dation will  depend  upon  the  use  to  which  the  floor  is  to  be  put,  and  upon 
the  character  of  the  material  upon  which  the  foundation  is  to  rest.  The 
excavation  should  be  made  to  solid  ground  or  until  there  is  depth 
enough  to  allow  a  sub-foundation  of  gravel  or  cinders.  Upon  this  base 
a  layer  of  cinders  or  gravel  6  to  8  inches  thick  is  placed  and  thoroughly 
rammed.  The  cement  concrete  base,  made  of  I  part  Portland  cement, 
3  parts  sand  and  5  to  6  parts  broken  stone  or  gravel,  is  then  placed  on 


CEMENT  FLOORS  283 

the  sub-foundation  and  thoroughly  rammed.  The  cement  and  sand 
should  be  mixed  dry  until  the  mixture  is  of  a  uniform  color,  the  gravel 
or  broken  stone  is  then  added,  having  previously  been  wet  down,  and 
the  concrete  is  thoroughly  mixed,  sufficient  water  being  added  during 
the  process  of  mixing  to  make  a  moderately  wet  concrete.  The  con- 
crete is  of  the  proper  consistency  if  the  moisture  will  just  flush  to  the 
top  when  the  concrete  is  thoroughly  rammed.  The  concrete  should  be 
mixed  until  the  ingredients  are  thoroughly  incorporated  and  each  par- 
ticle of  the  aggregate  is  thoroughly  coated  with  mortar. 

The  wearing  coat  is  usually  made  of  I  part  Portland  cement  and 
one  or  two  parts  of  clean  sharp  sand  or  granite  screenings  that  will  pass 
through  a  ^-inch  screen.  The  thickness  of  the  wearing  coat  will  de- 
pend upon  the  wear,  and  varies  from  3/2  to  2  inches  thick,  I  inch  being 
a  very  common  thickness.  The  mortar  for  the  wearing  surface  should 
be  rather  dry  and  should  be  applied  before  the  cement  in  the  concrete 
base  has  begun  to  set.  Care  should  be  used  to  see  that  there  is  not  a 
layer  of  water  on  the  upper  surface  of  the  base  or  that  a  film  of  clay 
washed  out  of  the  sand  or  gravel  has  not  been  deposited  on  the  sur- 
face, for  either  will  make  a  line  of  separation  between  the  base  and  the 
wearing  surface.  The  mortar  is  brought  to  a  uniform  surface  with  a 
straight  edge,  and  is  rubbed  and  compressed  with  a  float  to  expel  the 
water  and  air  bubbles.  As  the  cement  sets  it  is  rubbed  smooth  with  a 
plastering  trowel.  Joints  should  be  formed  in  the  floor  making  it  into 
blocks  about  4  to  8  feet  square. 

Cement  floors  are  said  to  be  a  failure  for  railway  round  houses  for 
the  reason  that  they  flake  and  crack  after  they  have  been  used  a  short 
time,  on  account  of  the  varying  changes  to  which  they  are  subjected. 

Cement  floors  vary  in  cost,  depending  upon  the  thickness  of  the 
floor  and  upon  local  conditions.  In  central  Illinois  a  cement  floor  hav- 
ing a  i -inch  surface  coat  and  3  inches  of  concrete  laid  on  a  cinder 
foundation  6  to  8  inches  thick  can  be  obtained  (1903)  for  about  12 
cents  per  square  foot.  A  very  substantial  concrete  floor  can  usually 
be  obtained  for  about  20  cents  per  square  foot. 


20 


284  FLOORS 

Tar  Concrete  Floors. — The  following  specifications  for  tar  con- 
crete floors  are  given  in  circulars  Nos.  54  and  55  of  the  Boston  Man- 
ufacturer's Mutual  Fire  Insurance  Co.,  and  are  reprinted  in  Engineer- 
ing News,  March  21,  1895. 

"The  floor  to  be  6  inches  thick,  and  to  be  put  down  as  follows :  The 
iower  5  inches  to  be  of  clean  coarse  gravel  or  broken  stone,  with  sufficient 
fine  gravel  to  nearly  fill  the  voids,  thoroughly  coated  with  coal-tar  and 
well  rammed  into  place.  On  this  place  a  layer  I  inch  thick  of  clean, 
fine  gravel  and  sand  heated  and  thoroughly  coated  with  a  mixture  of 
coal-tar  and  coal-tar  pitch  in  the  proportions  of  I  part  of  pitch  and  2 
parts  of  tar.  This  layer  is  to  be  rolled  with  a  heavy  roller  and  brought 
to  a  true  and  level  surface  ready  to  receive  the  floor  plank.  No  sand  or 
gravel  to  be  used  while  wet. 

"A  floor  of  the  kind  above  specified  should  always  be  protected  by 
a  floor  of  wood  over  it,  and  the  plank  should  be  laid  and  bedded  in  the 
top  surface  while  it  is  warm  and  before  it  becomes  hard. 

"For  light  work  the  thickness  of  the  lower  layer  of  concrete  may  be 
reduced  one  or  more  inches  if  upon  a  dry  gravelly  or  sandy  soil.  For 
storage  purposes  where  the  articles  stored  are  light  and  trucks  are 
little  used,  the  following  specification  has  been  found  to  give  a  satis- 
factory floor: 

"The  lower  layer  being  mixed  and  put  down  as  above  specified,  the 
top  layer  will  be  of  fine  gravel  and  sand,  heated  and  thoroughly  mixed 
with  a  mixture  of  equal  parts  of  coal-tar,  coal-tar  pitch  and  paving 
cement,  so  that  each  particle  of  sand  and  gravel  is  completely  coated 
with  the  mixture,  using  not  less  than  one  gallon  of  the  mix- 
ture to  each  cubic  foot  of  sand  and  gravel.  This  layer  should  be  well 
rolled  with  a  heavy  roller  and  allowed  to  harden  several  days  before  be- 
ing used." 

Brick  Floors. — Brick  floors  are  recommended  as  the  most  satis- 
factory floors  for  round  houses.  Round  house  floors  on  the  Boston  & 
Maine  R.  R.  are  made  as  follows :  *Brick  is  laid  flat  on  a  2-inch  layer  of 
bedding  sand  on  well  compacted  earth,  gravel  or  cinders.  Joints  are  left 
open  y%  of  an  inch  and  are  swept  full  of  cement  grout. 

Round  house  floors  are  made  on  the  Chicago,  Milwaukee  &  St.  Paul 
R.  R.,  as  follows:  *Vitrified  brick  is  laid  on  edge  on  a  layer  of  sand  I 


*Eighth  Annual  Report  of  the  Association    of    Railway    Superintendents    of 
Bridges   and   Buildings. 


WOODEN  FLOORS  285 

to  2  inches  thick  on  a  cinder  foundation  6  inches  thick.    Fine  sand  is 
broomed  into  the  cracks  after  the  brick  are  in  place. 

The  cost  of  this  floor  per  square  yard  is  about  as  follows : 
Material. 

Firebox  cinders  cost  nothing $00.00 

Paving  brick o .  50 

Labor. 

Preparing  the  foundation o .  20 

Laying  the  brick o.  15 


Total  cost  per  square  yard .$0.85 

Total  cost  per  square  foot 9^2  cents. 

The  cost  of  brick  floors  as  given  in  the  reports  of  the  Association 
of  Railway  Superintendents  of  Bridges  and  Buildings  varies  from  <)l/2 
to  13  cents  per  square  foot. 

The  Southern  &  Southwestern  Railway  Club — Eng.  News,  Jan.  16, 
1896 — recommends  that  round  house  floors  be  made  of  vitrified  brick 
laid  as  follows :  Make  a  bed  surface  of  slag  or  chert  about  18  inches 
thick,  then  put  a  coat  of  sand  over  slag,  lay  brick  on  edge  and  level 
them  up  by  tamping.  After  this  is  done  a  coat  of  hot  tar  is  applied 
which  enters  the  space  between  the  bricks  and  cements  them  together. 

Wooden  Floors. — Coal-tar  or  asphalt  concrete  makes  the  best 
foundation  for  a  shop  floor.  If  Portland  cement  is  used,  the  planking 
will  decay  very  rapidly  unless  the  top  of  the  concrete  is  mopped  with 
coal-tar  or  asphalt.  A  floor  laid  by  Pratt  &  Whitney  Co.,  of  Hartford, 
Conn.,  is  described  as  follows:  'In  laying  a  basement  floor  about  18 
years  since  of  10,000  square  feet,  8,000  square  feet  were  laid  over  coal- 
tar  and  pitch  concrete  in  about  equal  proportions,  and  about  2,000  square 
feet  were  laid  over  cement  concrete.  The  latter  portion  of  the  floor 
was  removed  in  about  ten  years,  the  timbers  and  the  plank  being  com- 
pletely rotted  out;  while  the  other  was  in  a  perfect  state  of  preserva- 
toin  and  has  continued  so  until  the  present  time."  The  floor  wdth  tar 
concrete  foundations  was  constructed  as  follows:  "Excavation  was 
made  about  one  foot  below  the  floor  and  six  inches  of  coarse  stone 


286  FLOORS 

was  filled  in,  then  five  inches  of  concrete  made  of  coarse  gravel,  coal- 
tar  and  pitch,  and  finally  about  one  inch  of  fine  gravel  tar  concrete. 
Before  the  concrete  was  laid,  heavy  stakes  were  driven  about  three  feet 
apart  to  which  the  4"  x  4"  floor  timbers  were  nailed  and  leveled  up. 
The  concrete  was  then  filled  in  around  the  floor  timbers  and  thoroughly 
tamped.  A  layer  of  hot  coal-tar  was  then  spread  on  top  of  the  concrete 
and  the  flooring  was  laid  and  nailed  to  the  timbers.  It  is  very  es- 
sential that  the  gravel  be  perfectly  dry  before  mixing;  and  this  is  ac- 
complished by  mixing  it  with  hot  coal-tar.  What  is  known  as  dis- 
tilled or  refined  coal-tar  must  be  used  as  that  which  comes  from  the 
gas  house  without  being  refined  does  not  work  in  a  very  satisfactory 
manner." 

The  following  paragraph  is  abstracted  from  Report  No.  V.,  Insur- 
ance Engineering  Experiment  Station,  Boston,  Mass  : 

"Floors  over  an  air  space  or  on  cement  are  subject  to  a  dry  rot. 
Asphalt  or  coal-tar  concrete  is  softened  by  oil,  and  the  dust  will  wear 
machinery  unless  the  concrete  is  covered  by  plank  flooring.  Floors 
made  by  laying  sleepers  on  6  inches  of  pebbles,  tarred  when  hot,  then 
2  inches  tarred  sand  packed  flush  with  the  top  of  the  sleepers,  and  cov- 
ered with  a  double  flooring,  have  remained  sound  for  37  years.  Double 
flooring  at  right  angles  can  be  laid  on  concrete  without  the  use  of 
sleepers.  It  is  usually  preferable  to  secure  nailing  strips  to  stakes  4 
feet  apart  each  way  and  driven  to  grade,  concrete  flush  to  top  of  strips, 
and  lay  1^2  -inch  flooring." 

The  floor  shown  in  Fig.  135  was  laid  in  an  extensive  shop  on  the 
Boston  &  Maine  Railway.  The  earth  was  well  compacted  and  brought 
to  a  proper  surface  and  a  4-inch  bed  of  coal-tar  concrete  put  down  in 


Transverse 


^  £  Roofing  Pitch 
""-  Compacted  Earfh 

FIG.  135. 


WOODEN  FLOORS  287 

three  courses.  The  stones  in  the  lower  course  were  to  be  not  less  than 
I  inch  in  diameter.  Stones  in  each  course  were  well  covered  with  tar 
before  laying  and  were  well  tamped  and  rolled  afterwards.  The  third 
and  finishing  course  was  composed  of  good  clean  sharp  sand  well  dried, 
heated  hot  and  mixed  with  pitch  and  tar  in  proper  proportions.  This 
was  then  carefully  rolled  and  brought  to  a  true  level  to  fit  a  straight 
edge.  On  the  finished  surface  of  the  foundation  was  spread  a  coating 
^4-inch  thick  of  best  roofing  pitch  put  on  hot  and  into  which  the  lower 
course  of  the  plank  was  laid  before  the  pitch  cooled. 

Care  was  taken  to  have  the  planks  thoroughly  bedded  in  the  pitch 
and  after  laying,  the  joints  were  filled  with  pitch.  If  vacant  spaces 
appeared  under  the  plank,  they  were  filled  up  with  pitch  by  boring 
through  the  plank.  The  cost  of  this  flooring  wras  about  18  cents  per 
square  foot,  using  spruce  lumber. 

A  cheap  but  serviceable  floor  may  be  made  as  shown  in  Fig.  136. 
The  soil  is  excavated  to  a  depth  of  12  to  15  inches  and  cinders  are  filled 
in  and  carefully  tamped.  The  flooring  planks  are  nailed  to  the  sills 
which  are  bedded  in  the  cinders.  The  life  of  the  plank  flooring  can  be 
increased  by  putting  a  coating  of  slaked  lime  on  top  of  the  cinders. 


FIG.  136. 

The  floor  shown  in  Fig.  137  was  used  in  the  factory  of  the  Atlas 
Tack  Company,  Fairhaven,  Mass.,  and  needs  no  explanation. 


^-/ 

/'  ^S'rfem/ock 

i 

_£ 


'  £'      "        Transverse 


FIG.  137. 


288  FLOORS 

A  very  good  floor  for  mills  and  factories  is  shown  in  Fig.  138. 

'  %" Mafc/tetf  Afap/e  Long/fud/na/ 


^~f  f/ne  Concrete  of  tar  or  asp  ha  ft 


The  pitch  or  asphalt  will  prevent  the  decay  of  the  plank  and  will 
add  materially  to  the  life  of  the  floor.  Maple  flooring  makes  the  best 
wearing  surface  for  floors  and  should  be  used  if  the  cost  is  not  pro- 
hibitive. 

The  floor  shown  in  Fig.  139  was  constructed  as  follows :  Two-inch 
plank,  matched  and  planed  on  one  side,  were  laid  on  3"  x  3"  chestnut 
joists.  The  surface  of  the  cinders  was  kept  2"  away  from  the  wood  and 


this  space  was  filled  with  lime  mortar.  After  the  surface  of  the  cin- 
ders had  been  graded,  the  3"  x  3"  joists  were  held  in  place  by  stakes 
nailed  to  the  joists  about  three  feet  apart.  The  lime  mortar  was  then 
filled  in  around  and  slightly  above  the  surface  of  the  joists  to  allow  for 
shrinkage.  Before  laying  the  floor  a  thin  layer  of  slaked  lime  was 
spread  over  the  surface.  This  floor  in  an  eastern  city  cost  about  85 
cents  per  square  yard;  and  has  a  life  of  10  to  12  years. 

Examples  of  Floors. — The  floor  of  the  Locomotive  Shop  of  the 
A.  T.  &  S.  F.  R.  R.,  at  Topeka,  Kas.,  is  as  follows :  The  floor  foun- 
dation is  formed  of  6  inches  of  concrete  resting  on  the  natural  soil  well 
tamped.  On  the  concrete  are  laid  3"  x  4"  yellow  pine  stringers  at  18- 
inch  centers,  the  whole  being  covered  with  2-inch  No.  I  hard  maple, 
surfaced  on  one  side  and  two  edges  and  milled  for  y^"  x  i"  pine  splines. 


EXAMPLES  OF  FLOORS  289 

The  flooring  in  the  Great  Northern  Shops  at  St.  Paul,  Minn.,  is 
3"  x  12"  plank  on  6"  x  8"  sleepers  bedded  in  18  inches  dry  sand  filling. 

The  floor  of  the  locomotive  shops  of  the  Philadelphia  and  Reading 
R.  R.,  is  made  of  bituminous  concrete  on  which  are  a  solid  course  of 
3"  x  8"  hemlock  and  a  top  wearing  surface  of  1%"  x  4"  maple. 

The  machine  shop  floors  of  the  Lehigh  Valley  R.  R.  at  Sayre  Pa., 
are  of  concrete  with  a  maple  wearing  surface  in  the  high  grade  buildings 
and  yellow  pine  in  the  others. 

The  Southern  Railway  has  a  vitrified  brick  floor  in  a  round  house 
at  Knoxville,  Tenn.,  which  is  giving  good  satisfaction.  The  cost  of  this 
floor  was  about  $1.00  per  square  yard. 

Shop  floors  for  the  American  Locomotive  Works,  Schenectady, 
N.  Y.,  are  described  in  Engineering  Record,  May  30,  1903  ,as  follows : 

"On  a  sand  fill  was  laid  from  4  to  6  inches  of  2^-inch  broken  stone, 
rammed  dry  and  then  flushed  with  about  one  gallon  of  hot  tar  for 
every  square  yard  of  floor.  This  course  was  covered  with  2  inches  of 
hot  sand  and  tar  mixed  to  the  consistency  of  dry  mortar,  shoveled  into 
place  and  thoroughly  rammed  to  a  level  surface.  Spiking  strips  made 
of  3"  x  4"  timbers  were  imbedded  in  the  sand  at  about  3-ft.  centers.  To 
these  strips  were  spiked  2-in.  rough  hemlock  planks,  which  were  in 
turn  covered  with  transverse  tongued  and  grooved  %-in.  maple  boards 
4  inches  wide." 

Cedar  Blocks  form  a  neat,  clean  and  durable  floor.  Care  should 
be  used  where  heavy  jacking  is  to  be  done  on  wooden  block  floor 
that  the  blocks  are  not  forced  down  through  the  plank  foundation. 

A  cedar  block  floor  in  the  Chicago  Ave.  round  house  of  the  C  & 
N.  W.  R.  R.,  laid  on  planks  on  a  gravel  foundation  cost  about  1 1  cents 

9 

per  square  foot. 

*A  cedar  block  floor  on  the  C.  &  E.  I.  R.  R.,  laid  directly  on  a 
gravel  foundation  cost  8  cents  per  square  foot. 

*A  floor  constructed  of  6  to  8-inch  blocks  sawed  from  old  bridge 
timbers,  set  on  2-inch  hemlock  plank,  which  in  turn  rested  on  3  inches 

•Reports  Association  of  Railway  Superintendents  of  Bridges  and  Buildings. 


290  FLOORS 

of  dry  gravel  or  sand,  has  been  used  on  the  Ashland  division  of 
the  C.  &  N.  W.  R.  R.,  and  cost  about  4  cents  per  square  foot  exclusive 
of  the  cost  of  the  old  timbers.  This  floor  has  proved  to  be  quite  satis- 
factory. 

FLOORS  ABOVE  GROUND.— The  type  of  floor  used  for  the 
upper  stories  of  mill  buildings  will  depend  upon  the  character  of  the 
structure  and  the  use  to  which  the  floor  is  to  be  put.  In  fireproof  build- 
ings the  floors  should  preferably  be  constructed  of  fireproof  materials, 
although  there  is  comparatively  little  risk  from  fire  under  ordinary 
conditions  with  a  heavy  plank  floor.  Where  the  load  on  the  floor  is 
very  heavy  some  form  of  trough  or  buckled  plate  floor  is  very  often 
used. 

Timber  Upper  Floors. — Where  steel  floor  beams  are  used  the 
floor  is  often  made  by  placing  2"  x  6"  or  2"  x  8"  planks  on  edge  and 
spiking  them  together,  the  wearing  surface  being  made  of  hard  wood 
boards.  Where  there  is  much  danger  from  fire  this  floor  can  be  fire- 
proofed  by  plastering  it  below  with  wire  lath  and  hard  plaster  and  by 
putting  a  layer  of  cement  or  lime  mortar  between  the  plank  and  the 
wearing  surface.  The  upper  surface  is  also  sometimes  finished  with  a 
wearing  coat  of  cement  or  asphalt. 

The  standard  floor  recommended  by  the  Boston  Manufacturer's 
Mutual  Fire  Insurance  Co.,  for  mill  buildings  constructed  of  heavy 
timbers,  calls  for  a  layer  of  spruce  plank,  generally  3  inches  thick,  laid 
to  cover  two  floor  beam  spaces  and  breaking  joints  every  3  feet;  on  this 
are  laid  3  thicknesses  of  rosin  sized  paper,  each  layer  being  mopped 
with  tar.  The  top  floor  is  ij/g-in.  hard  wood,  preferably  maple.  The 
main  beams  are  spaced  8  to  10  feet.  "The  floor  is  smoother  if  laid 
across  the  line  of  the  plank  in  the  under  floor,  but  traveling  loads  are 
better  distributed  when  moved  in  and  out  of  the  store  house  if  the  top 
floor  is  laid  parallel  to  the  lower  plank." 

Brick  Arch  Floor. — The  brick  arch  floor  shown  in  Fig.  140  was 
formerly  much  used  in  fireproof  buildings  and  is  still  used  to  some  ex- 
tent in  mills  and  factories.  The  arch  is  commonly  made  of  a  single 


FIREPROOF  FLOORS 


291 


Brick  Arch  Consfruction 

FIG.  140. 

layer  of  brick  about  4  inches  thick,  with  a  span  of  4  to  8  feet  and  a  cen- 
ter rise  of  preferably  not  less  than  ^  the  span.  The  space  above  the 
brick  arch  is  filled  with  concrete  and  a  wearing  floor  is  nailed  to  strips 
imbedded  in  the  surface  of  the  concrete.  The  most  desirable  span  is 
from  4  to  6  feet.  Tie  rods  are  commonly  placed  at  about  Yz  the  height 
of  the  beam  and  are  spaced  from  4  to  6  feet  apart.  The  thrust  of  the 
arch  per  lineal  foot  can  be  found  by  the  formula 

_   1.5   W  L- 
R 

where  T  =  thrust  of  arch  in  Ibs.  per  lineal  foot; 
W  =  load  on  arch  in  Ibs.  per  square  foot ; 
L  =  span  of  the  arch  in  feet ; 
R  =  rise  of  arch  in  inches. 

The  weight  of  this  floor  is  about  75  Ibs.  per  square  foot. 
Corrugated  Iron  Arch  Floor. — The  corrugated  iron  arch  shown 
in  Fig.  141  makes  a  very  strong  floor  for  shops  and  mills.  The  cor- 
rugated iron  acts  as  a  center  for  the  concrete  filling  above  it,  and  in 
connection  with  the  concrete  makes  a  composite  arch.  The  corrugated 
iron  or  steel  is  ordinarily  the  standard  2*^ -inch  corrugations,  and  the 
gages  are  Nos.  16,  18  or  20,  depending  upon  the  load  and  the  length  of 
span.  The  rise  of  the  arch  should  not  be  less  than  1-12  the  span  and 


Corrugated  Iron  Arch 

FIG.  141. 


292 


FLOORS 


should  have  a  thickness  of  from  2  to  4  inches  of  concrete  over  the  cen- 
ter of  the  arch.  Beams  are  spaced  from  4  to  7  feet  apart  for  this  floor, 
and  tie  rods  are  used  as  in  the  brick  arch  floor. 

Expanded  Metal  Floors. — The  floor  shown  in  Fig.  142  is  con- 
structed as  follows :  A  wood  centering  is  suspended  from  the  beams, 
with  the  upper  surface  of  the  centering  about  I  inch  below  the  top  of 
the  beams,  a  layer  of  expanded  metal  is  stretched  across  the  beam 
in  sheets  and  the  concrete  is  spread  over  and  tamped  so  that  the  ex- 
panded metal  becomes  imbedded  in  the  lower  inch  of  the  concrete.  The 


FIG.  142. 

concrete  is  usually  made  of  I  part  Portland  cement,  2  parts  sand  and 
6  parts  cinders,  and  weighs  80  to  90  pounds  per  cubic  foot.  Beams 
were  formerly  spaced  from  5  to  8  feet  apart,  but  have  recently  been 
spaced  much  farther;  spacings  as  wide  as  18  to  20  feet  having  been 
successfully  employed.  Expanded  metal  \vith  3-inch  mesh  cut  from  No. 
10  gage  sheet  steel  is  commonly  used  for  floors,  which  are  made 
from  3  to  5  or  6  inches  thick.  For  the  design  of  expanded  metal  and 
other  forms  of  reinforced  concrete  floors,  see  the  author's  "  The  Design 
of  Highway  Bridges."  The  companies  controlling  the  patents  on  this 
material  will  furnish  gratis,  data  and  tables  for  the  design  of  expanded 
metal  floors.  Examples  of  floors  may  be  found  by  consulting  the 
Engineering  News,  Engineering  Record,  etc. 

Expanded  metal  floors  are  also  made  as  shown  in  Fig.  143.    This 
type  is  adapted  to  very  heavy  floor  loads.    The  arch  should  have  a  rise 


FIG.  143. 


ROEBUNG  FLOOR 


293 


of  i-io  to  y%  the  span.  Tests  have  shown  that  the  steel  work  in  ex- 
panded metal  floors  is  not  ordinarily  affected  by  the  cinder  concrete.  If 
care  is  used  when  erecting  the  floor  to  coat  the  expanded  metal  with  a 
coating  of  Portland  cement  mortar  before  the  metal  has  become  rusted. 
the  protection  against  corrosion  will  be  almost  perfect. 

Roebling  Floor. — The  floor  shown  in  (c)  Fig.  144  consists  of  a 
wire  cloth  arch,  stiffened  by  woven-in  stiff  steel  rods  ^  to  i-inch  in 
diameter,  at  about  9-inch  centers,  which  is  sprung  between  the  floor 
beams  and  abuts  on  the  seat  formed  by  the  lower  edge  of  the  floor  beam. 


"BUCKEYE"  FIREPROOF  FLOORING. 

(a) 


MULTIPLEX  STEEL  PLATE  FLOOR 


(b) 


Roebling    Fire-proof  System 
(C) 

FIG.  144. 


(d) 


On  this  wire  centering  Portland  cement  concrete  is  filled  in  and  is  fin- 
ished with  a  wearing  coat  of  cement  or  a  wgoden  floor  as  shown.  The 
beams  are  held  in  position  by  ^4  or  J  3 -inch  tie  rods,  placed  from  4  to 


294  FLOORS 

6  feet  apart.  The  concrete  is  commonly  composed  of  I  part  Portland 
cement,  2.]/2  parts  sand  and  6  parts  clean  cinders,  and  is  laid  with  a 
thickness  of  not  less  than  3  inches  over  the  crown  of  the  arch.  The 
weights  and  safe  loads  for  floors  constructed  on  this  system  are  given 
in  the  manufacturer's  catalog. 

The  Roebling  Construction  Company  also  makes  a  floor  with  flat 
construction  as  follows:  A  light  framework  is  made  of  flat  steel  bars 
set  on  edge  and  spaced  1 6-inch  centers,  with  %-turn  at  both  ends 
where  the  bars  rest  on  the  steel  beams ;  braces  of  half  round  iron  are 
spaced  at  intervals  to  brace  the  bars.  The  Roebling  standard  lathing 
with  %  -inch  steel  stiffening  ribs  woven  in  every  Jl/2  inches,  is  then 
applied  to  the  under  side  of  the  bars  and  laced  to  them  at  each  inter- 
section. On  this  wire  lathing  cinder  concrete  from  3  to  4  inches  thick 
is  deposited. 

"Buckeye"  Fireproof  Flooring. — The  steel  flooring  shown  in  (a) 
Fig.  144  is  manufactured  by  the  Youngstown  Iron  &  Stetl  Roofing  Co., 
Youngstown,  Ohio.  This  floor  is  made  in  two  sizes,  one  for  bridge 
floors  and  the  other  for  building  floors.  The  flooring  shown  in  (a)  is  for 
buildings,  is  made  in  sections  of  four  triangles  each  in  lengths 
up  to  10  feet,  and  will  lay  a  width  of  21  inches.  Each  triangle  is  5J4 
inches  wide  and  2l/2  inches  deep.  The  flooring  when  complete  with  a 
concrete  filling  and  a  il/2 -inch  wearing  surface  will  weigh  from  32  to 
35  pounds  per  square  foot.  The  weights  of  the  metal  troughs  laid  in 
place  are  given  in  the  following  table : 

WEIGHTS  OF  METAL  TROUGHS  2l/2  INCHES  DEEP  BY  5^4  INCHES  WIDE, 

INCLUDING    SIDE   LAPS. 

GALVANIZED  TROUGHS.  BLACK    IRON    TROUGHS. 

No.  16—386  Ibs.  per  100  square  feet.  No.  16—363  Ibs.    per    100     square    feet. 

NoT  17—350  "  "  "          "  "  No.  17—327      " 

No.  18—313  "  "  "          "  "  No.  18—290      " 

No.  19— 278  "  "  "  "  "  No.  19— 254      " 

No.  20—241  "  "  "          "  "  No.  20—218      " 

No.  22—204  "  "  "          "  "  No.  22—181  " 

No.  24—168  "  "  "          "    _  "  No.  24—145  " 


MISCELLANEOUS  FLOORS  295 

The  safe  loads  in  addition  to  the  weight  of  the  floor  as  given  in 
the  manufacturer's  catalog  are  given  in  the  following  table  : 


LOADS  FOR  "BUCKEYE"  FIREPROOF  FLOOR. 


Span. 

No.  18  Gage. 

No.  20  Gage. 

No.  22  Gage. 

No.  24  Gage. 

3  ft.  0  in. 

1050  Ibs. 

SOO  Ibs. 

580  Ibs. 

450  Ibs. 

3  "   6  " 

820  " 

570  " 

425  " 

320  " 

4  "   0  " 

675  " 

425  " 

315  " 

230  " 

4  "   6  " 

570  " 

320  " 

240  " 

190  " 

5  "   0  " 

475  " 

250  " 

180  " 

135  •• 

5  "   6  " 

200  " 

200  " 

140  " 

Multiplex  Steel  Floor.  —  The  steel  flooring  shown  in  (b)  Fig.  144, 
is  manufactured  by  the  Berger  Mfg.  Co.,  Canton,  Ohio.  This  floor  is 
made  with  corrugations  from  2  to  4  inches  deep  and  of  Nos.  16,  18,  20 
and  24  gage  steel.  The  triangles  are  filled  writh  concrete  and  the  floor 
is  given  a  cement  finish,  or  is  covered  with  a  wooden  wearing  surface. 
Tables  of  safe  loads  for  Multiplex  Steel  Floor  are  given  in  the  manu- 
facturer's catalog,  and  are  larger  than  for  the  "Buckeye"  Flooring  for 
the  same  span. 

Ferroinclave.  —  Ferroinclave  is  fully  described  in  Chapter  XIX. 
It  has  been  used  by  the  Brown  Hoisting  Company  for  floors  as  wrell  as 
for  roofing  and  siding.  It  should  make  a  very  satisfactory  flooring 
where  light  loads  are  to  be  carried. 

Corrugated  Flooring.  —  Corrugated  flooring  or  trough  plates 
shown  in  (a)  and  (b)  Fig.  145,  are  used  for  fireproof  floors  where  ex- 
tra heavy  loads  are  to  be  carried  in  mill  buildings,  in  train  sheds  and 
for  bridge  floors.  The  troughs  are  filled  with  concrete,  which  is  given 
a  finishing  coat  of  cement  and  sand  or  is  covered  with  a  plank  floor; 
the  planks  being  laid  directly  on  the  plates  or  spiked  fo  spiking  pieces 
imbedded  in  the  filling.  The  details,  weights  and  safe  loads  for  corrug- 
ated plates  are  given  in  Pencoyd  Iron  Works'  handbook,  in  Carnegie 
Steel  Company's  handbook,  and  in  Trautwine's  Pocket-book.  Details 
of  corrugated  plates  are  also  given  in  the  American  Bridge  Company's 
"Standards  for  Structural  Details." 


296  FLOORS 

Corrugated  flooring  or  trough  plates  are  usually  very  hard  to  get 
and  the  Z-bar  and  plate  floor  shown  in  (c)  Fig.  145,  and  the  angle  and 

Pencoyd  Corrugated  Flooring  7.  Bar  Floor  Angle  and  Plate  Floor 

(a)  ( b)  (C)  (d  \ 

FIG.  145. 

plate  floor  shown  in  (d)  are  substituted.  The  details,  weights  and  safe 
loads  for  Z-bar  and  plate  flooring  are  given  in  the  handbooks  above 
named.  Angle  and  plate  flooring  is  made  of  equal  legged  angles  and 
plates,  and  the  safe  loads  are  not  given  in  the  handbooks  but  must  be 
calculated.  The  moment  of  inertia,  I,  of  a  section  of  flooring  contain- 
ing two  angles  and  two  plates  is  given  by  the  formula 

I  =  2!'  +  2Ad2  +  2/" 

where  /'  =  moment  of  inertia  of  one  angle  about  an  axis  through  the 
center  of  gravity  of  the  angle  parallel  to  the  neutral  axis  of  the  flooring ; 
A  =  area  of  one  angle ; 

d  =  distance  from  center  of  gravity  of  the  angle  to  the  neutral 
axis  of  the  flooring; 

/"  =  moment  of  inertia  of  the  plate  about  the  neutral  axis. 

The  properties  of  the  angles  required  in  the  calculations  may  be 
obtained  from  the  handbooks,  and  /"  is  equal  to  one-half  the  sum  of  the 
moments  of  inertia  of  the  plate  about  its  long  and  its  short  diameter — 
since  the  sum  of  the  moments  of  inertia  about  any  pair  of  rectangular 
axes  is  a  constant. 

Buckled  Plates. — Buckled  plates  are  made  from  soft  steel  plates 
from  3  to  5  feet  wide,  and  are  from  *4  to  7~I6  inches  thick.  Buckled 
plates  are  made  in  lengths  having  from  one  to  15  buckles  or  domes  in 
one  plate.  Buckles  vary  in  depth  from  2  to  3^  inches,  however,  dif- 
ferent depths  should  not  be  used  in  the  same  plate.  Buckled  plates  are 
usually  supported  along  the  edges  and  the  ends  and  are  bolted  to  the 
floor  beams.  The  details,  weights  and  safe  loads  are  given  in  the  hand- 
books named,  above  and  in  the  Passaic  Steel  Company's  handbook.  The 


PLATE  FLOORING 


297 


buckled  plates  are  covered  with  concrete,  which  is  given  a  finishing  coat 
of  cement  or  is  covered  with  plank  flooring. 

Steel  Plate  Flooring.— Fireproof  floors  around  smelters,  etc.,  are 
often  made  of  steel  plates.  Flat  steel  plates  do  not  make  a  very  satis- 
factory floor  for  the  reasons  that  the  plates  will  bulge  up  in  the  cen- 
ter when  fastened  around  the  edges,  and  because  they  become  danger- 
ously smooth. 

Neverslip  Wrought  Steel  Floor  Plates  are  made  from  24"  x  72"  to  36" 
x  120",  and  from  3-16"  to  i"  thick.  These  plates  are  designed  to  take 
the  place  of  the  cast  iron  checkered  plates  formerly  used  for  floors, 
weigh  about  50  per  cent  less  and  last  much  longer.  The  stock  sizes, 
weights  and  safe  loads  for  Neverslip  floor  plates  are  given  in  the  Stock 
List  of  the  Scully  Steel  Co.,  Chicago.  These  lists  are  issued  about  six 
times  a  year  and  will  be  sent  free  upon  request. 

Thickness  of  Timber  Flooring. — The  thickness  of  white  pine 
and  spruce  flooring  for  different  spans  and  loads  is  given  in  Table 
XXXIIIa.  The  following  fibre  stresses  were  used  in  calculating  the 
thickness :  Transverse  bending,  1000  Ib. ;  end  bearing,  1000  Ib. ;  bear 
ing  across  the  fibre,  200  Ib. ;  shear  along  the  fibre,  100  Ib. 

TABLE  XXXIIIa. 
THICKNESS  OF  SPRUCE  AND  WHITE  PINE  PLANK  FOR  FLOORS. 


Span  in 
Feet. 

THICKNESS,  IN  INCHES,  FOE  VARIOUS  LOADS  PEE  SQUARE  FOOT  OF  PLANK. 

Ib. 
30 

Ib. 
40 

Ib. 
50 

Ib. 
75 

Ib. 

100 

Ib. 

125 

Ib.     Ib. 
1.50     175 

Ib.  1  Ib. 

200  225 

Ib. 

250 

Ib. 

275 

Ib. 

300 

Ib.  Ib. 
325  350 

Ib. 
375 

3.3 

<  i 

Ib. 
400 

4 

0.9 

1.1 

1  A 

1.2 

T  £ 

1.5 

T  ft 

1.7 

n  i 

1.9 

2.1 

2.2 

0    0 

2.4  2.5 

t  f\  t  n 

2.7 

2.8 

t  f 

2.9 

•>  T 

3.1  1  3.2 

3.4 

C 

5 1.2    1.4    1.5 


1.9   2.1 


2.4    2.6 


2.8    3.0   3.2    3.4 


3.5 


3.7    3.8    4.0   4.1    4.3 


6 1.4    1.6    1.8    2.2   2.6    2.9    3.1    3.4    3.6    3.8    4.0   4.2  i  4.4   4.6   4.8   4.9    5.1 


7 !  1.7  1.9  2.1  2.6  3.0  3.3    3.7    3.9    4.2    4.5    4.7    4.9   5.2    5.4   5.6    5.8 

8 1.9  2.2  2.4  3.0  3.4  3.8    4.4   4.5    4.8    5.1    5.4    5.7    5.9 1 6.1 

9 !2.1  2.5,2.7  3.4  3.9  4.3    4.7    5.1    5.4    5.8    6.1 

10 '2.4  2.7  3.1  3.7  4.314.8    5.2    5.6   6.0  

11 2.6  3.0  3.4  4.1  4.7  5.3    5.8 

12 2.9  3.3  3.7  4.5  5.2 

13 3.1  3.6  4.0  4.9  5.6 

14 3.4  3.9  4.3  5.3  6.1  .. 


6.0 


For  yellow  pine  use  nine-tenths  of  the  above  thicknesses. 


CHAPTER  XXIII. 
WINDOWS  AND  SKYLIGHTS. 

Glazing. — For  glazing  windows  and  skylights,  two  substances, 
glass  and  translucent  fabric  are  in  common  use. 

GLASS. — The  principal  kinds  of  glass  used  in  windows  and  sky- 
lights are  (i)  plane  or  sheet  glass ;  (2)  rough  plate  or  hammered  glass  ; 
(3)  ribbed  or  corrugated  glass;  (4)  maze  glass;  (5)  wire  glass — glass 
with  wire  netting  pressed  into  it ;  (6)  ribbed  wire  glass ;  and  (7)  prisms. 

(1)  Plane  Glass. — Plane  or  common  window  glass  is  technically 
known  as  sheet  or  cylinder  glass.    It  is  made  by  dipping  a  tube  in  molten 
glass  and  blowing  the  glass  into  a  cylinder,  which  is  then  cut  and 
pressed  out  flat.    Without  regard  to  quality  sheet  glass  is  divided  ac- 
cording to  thickness  into  "single  strength"  and  "double  strength"  glass. 
Double  strength  glass  is  ^-inch  thick  while  single  strength  glass  is 
about  i-i6-inch  thick.     In  mill  buildings,  lights  larger  than  12"  x  14" 
are  usually  made  of  double  strength  glass.    With  reference  to  quality 
sheet  glass  is  divided  into  three  grades  A  A,  A,  and  B.    The  A  A  is  the 
best  quality,  the  A  is  good  quality  while  the  B  is  very  poor.    The  B 
grade  is  suitable  only  for  stables,  cellars,  etc.     For  residences,  offices, 
and  similar  purposes  nothing  poorer  than  AA  should  be  specified.    The 
A  grade  does  very  well  for  ordinary  mills,  although  the  AA  grade 
should  be  used  if  practicable. 

(2)  Plate  Glass. — Plate  glass  is  made  by  casting  and  not  by 
blowing,  and  is  finished  by  grinding  and  polishing  on  both  sides  until 
a  smooth  surface  is  obtained.     It  is  usually  %  or  3-16  inches  thick. 
The  price  depends  upon  the  size  of  the  plate  and  the  quality  of  the  glass. 
The  rough  plate  glass  used  in  mills  is  not  finished  as  carefully  as  for 
glass  fronts,  and  it  may  contain  many  flaws  that  would  not  be  allow- 


KINDS  OF  GLASS 


299 


able  in  the  former  case.  The  roughened  surface  of  the  glass  prevents 
the  entrance  of  direct  sunlight  and  does  away  with  the  use  of  sun- 
shades. The  only  value  of  rough  plate  glass  is  in  softening  the  light, 
the  loss  of  light  in  passing  through  it  being  very  great. 

(3)  Ribbed  or  Corrugated  Glass. — Ribbed  or  corrugated  glass  is 
usually  smooth  on  one  side  and  has  5,  7,  n  or  21  ribs  on  the  other  side, 
(a)  Fig.  146.  It  varies  in  thickness  and  shape  of  ribs.  "Factory 
ribbed  "  glass  with  21  ribs  to  the  inch  is  distinctly  the  most  effective. 


Rfbhed 
(CO 


Figured 

(b) 

FIG.  146. 


Sheet  Prism 
(0 


(4)  Maze  Glass. — Maze  glass  has  one  side  smooth  and  has  a 
raised  pattern  on  the  other  side  roughening  practically  the  entire  sur- 
face, (b)  Fig.  146.     It  is  quite  effective. 

(5)  Wire  Glass. — Wire  glass  is  made  by  pressing  wire  netting 
into  the  molten  glass.     It  is  made  either  plane  or  with  ribs  or  prisms 
on  one  side.    Wire  glass  is  injured  but  not  destroyed  by  the  action  of 
fire  and  water,  and  is  now  accepted  by  insurance  companies  as  fire- 
proof construction. 

(7)  Prisms. — Prisms  are  made  in  small  sections  which  are  set 
in  a  frame  of  lead  or  other  metal,  or  are  made  in  sheets  as  shown  in  (c) 
Fig.  146.  Luxfer  sheet  prisms,  manufactured  by  the  American  Luxfer 
Prism  Co.,  Chicago,  will  be  cut  in  any  size  desired  up  to  84  inches  wide 
(parallel  with  the  saw  teeth)  by  36  inches  high. 

Diffusion  of  Light.* — The  light  entering  a  room  through  a  win- 
dow or  skylight  comes  for  the  most  part  from  the  sky  and  has,  there- 
fReport  No.  III.  Insurance  Engineering  Experiment  Station,  Boston, 


Mass. 


21 


300 


WINDOWS  AND  SKYLIGHTS 


fore,  a  general  downward  direction,  varying  with  the  time  of  day  and 
the  position  of  the  window.  The  portion  of  the  room  which  receives 
the  most  light  ordinarily  is  the  floor  near  the  windows,  but  if  we  inter- 
pose a  dispersive  glass  in  this  beam  the  light  will  no  longer  fall  to  the 
floor  but  will  be  spread  out  into  a  broad  divergent  beam  falling  with 
nearly  equal  intensity  on  walls,  ceiling  and  floor.  There  is  of  course 
no  gain  in  the  total  amount  of  light  admitted,  the  light  being  simply 
redistributed,  taking  up  from  the  floor  that  which  fell  there  and  was 
comparatively  useless,  and  sending  it  where  it  is  of  more  service. 

Experiments  have  shown  that  the  diffusion  of  light  in  a  room  lighted 
by  means  of  windows  or  skylights  depends  upon  the  kind  and  position 
of  the  glass  used.  The  relative  intensity  of  the  light  admitted  in  per 
cents  of  the  light  outside  the  window  for  plane  glass,  factory  ribbed 
glass,  Luxfer  and  canopy  prisms  is  shown  in  Fig.  147*. 


$+ 


Variation  of  Liqht 

with 
Angle  of  Skylight 

No  Direct  Sunlight 


^6\C 


30°   40°    50°    60°    70°    8O° 

Angle  skylight  makes  with  horizontal 
FIG.  147. 


Fig.  147  shows  a  great  increase  in  efficiency  of  factory  ribbed  glass 
and  prisms  as  the  sky  angle  diminishes. 


*Report  No.  III.     Insurance  Engineering  Experiment  Station,  Boston,  Mass. 


RELATIVE  VALUE  OF  DIFFERENT  KINDS  OF  GLASS 


301 


The  equivalent  areas  required  to  give  the  same  intensity  of  light 
with  the  kinds  of  glass  shown  in  Fig.  147,  are  given  in  Table  XXIV 
for  sky  angles  of  30°  and  60°. 

TABLE  XXIV. 
EQUIVALENT  AREAS  FOR  DIFFERENT  KINDS  OF  GLASS. 


Kinds  of  Glass. 

Angle  Skylight  makes  with  the  Horizontal. 

30° 

60° 

Plane 
Factory  Ribbed 
Luxfer  Prisms 

100  sq.  ft. 
25    "     " 

17    "     " 

100  sq.  ft. 
40    "    " 

30    "     " 

Luxfer  Canopy  Prisms 

13    "     " 

The  American  Luxfer  Prism  Co.,  recommends  that  Luxfer  prisms 
be  set  at  an  angle  of  about  57  degrees  with  the  vertical  when  used  in 
skylights. 

Relative  Value  of  Different  Kinds  of  Glass. — Ground  glass  is  of 
little  value  except  as  a  softening  medium  for  bright  sunlight.  It  be- 
comes opaque  with  moisture  and  makes  an  undesirable  window  glass. 
Roughened  plate  glass  has  very  little  value  as  a  diffusing  medium.  Of 
the  ribbed  glasses,  the  factory  ribbed  glass  with  21  ribs  to  the  inch  gives 
the  widest  and  most  uniform  distribution  and  is  distinctly  the  best. 
There  is  no  apparent  gain  in  corrugating  both  sides.  Ribbed  wire  glass 
is  about  20  per  cent  less  effective  than  the  factory  ribbed  glass.  When 
a  glass  of  a  slightly  better  appearance  than  the  factory  ribbed  glass  is 
wanted  the  maze  glass  is  the  best ;  the  raised  pattern  imprinted  on  the 
back  of  this  glass  giving  wide  diffusion,  especially  in  bright  sunlight. 
The  prisms  are  very  much  more  effective  than  any  of  the  glasses  men- 
tioned above,  but  their  cost  prevents  their  use  under  ordinary  conditions. 

Kind  of  Glass  to  Use. — Where  the  amount  of  skylight  is  large 
and  the  light  is  not  obstructed  by  buildings  plane  glass  is  very  satisfac- 
tory. Where  a  superior  light  is  desired,  or  where  the  skylight  area  is 
less  than  ample,  use  factory  ribbed  glass  in  skylights  and  in  the  upper 


302 


WINDOWS  AND  SKYLIGHTS 


panes  of  windows.  Where  the  skylight  area  is  very  small,  the  light  is 
obstructed,  or  a  very  superior  light  is  desired,  use  prisms.  Wire  glass 
should  be  used  where  there  is  danger  from  fire  and  in  skylights,  where 
it  removes  the  necessity  of  stretching  wire  netting  under  the  glass  to 
protect  it  and  to  prevent  it  from  falling  into  the  building  when  broken. 
Placing  the  Glass. — Factory  ribbed  glass  is  somewhat  more  ef- 
fective if  the  ribs  are  placed  horizontal,  but  the  lines  of  light  deflected 
from  the  horizontal  ribs  may  become  injurious  to  the  workmen's  eyes 
and  it  is  now  the  custom  to  set  the  ribs  vertical.  Ribbed  glass  should 
have  the  ribs  on  the  inside  for  ease  in  keeping  it  clean,  and  where  double 
glass  is  used  the  ribs  should  face  each  other  and  be  crossed.  Care  should 
be  used  in  setting  thick  wire  glass  in  metal  frames;  the  lower  edge 
must  bear  directly  on  the  frame,  but  the  top  and  sides  should  fit  loosely 
so  that  the  differential  expansion  of  the  glass  and  frame  will  not  crack 
the  glass.  Plane  glass  and  small  panes  of  other  kinds  of  glass  are 
set  with  glaziers'  tacks  and  putty.  In  skylights  and  large  windows 
some  method  must  be  used  that  will  allow  the  glass  to  expand  and  con- 
tract freely  and  at  the  same  time  will  be  free  from  leakage.  Several 
methods  of  glazing  skylights  without  putty  are  shown  in  Fig.  148. 
Skylight  bar  (a)  manufactured  by  Vaile  &  Young,  Baltimore  Md.,  is 
made  of  heavy  galvanized  iron  and  lead. 


(a) 


(e) 


Bars  (b)  and  (c)  are  made  of  zinc  or  galvanized  iron,  supported  by 
a  steel  bar.  Bar  (d)  is  adapted  to  small  panes  of  glass  and  is  made 
of  galvanized  iron;  it  is  made  water  tight  by  the  use  of  putty.  The 
skylight  bars  in  Fig.  148,  all  have  condensation  gutters  to  catch  the 
moisture  that  leaks  through  or  forms  on  the  inner  surface  of  the  glass. 


USE  OF  WINDOW  SHADES 


("  TL  iff  rT  *"?" 


Side 
Elevation 


(00 


FIG.  149. 


The  glass  in  a  large  greenhouse  at  Edgely  Pa.,  was  secured  to  the 
sash-bars  as  shown  in  (a),  Fig.  149.  It  will  be  seen  that  the  glass  is  im- 
bedded in  putty  on  the  under  side  only,  and  that  any  water  that  can  pos- 
sibly leak  through  between  the  bar  and  the  glass  will  be  caught  in 
the  drip  trough  "a",  and  be  carried  to  the  eaves.  The  lights  are 
1 6"  x  24"  and  the  sash-bars  are  spaced  24^  ins.,  c.  to  c.  The  lights 
are  held  in  place  by  two  patent  glazing  points  per  light,  driven  in  such 
a  way  as  to  prevent  the  glass  from  moving.  The  lights  overlap  but 
i-i6-in.,  the  leakage  having  been  found  to  be  smaller  and  less  liable  to 
occur  with  this  than  with  a  larger  lap. 

The  Paradigm  system  of  glazing  is  shown  in  (b)  Fig.  149.  This 
system  is  in  use  in  a  large  number  of  shops,  among  which  the  steam 
engineering  buildings  for  the  Brooklyn  Navy  Yard,  described  in  Part 
IV,  is  one  of  the  best  examples.  The  patents  for  the  Paradigm  skylight 
are  controlled  by  Arthur  E.  Rendle,  New  York. 

Skylights  are  of  two  types;  (i)  box  skylights  covering  a  small 
area  and  placed  on  a  curb  raising  the  glass  above  the  roof,  and  (2) 
continuous  skylights  usually  placed  in  the  plane  of  the  roof.  The  glass 
used  for  skylights  varies  from  ^4  to  */g  inch  thick  and  should  preferably 
be  wire  glass.  The  glass  used  for  skylights  usually  comes  in  sheets 
about  20  inches  wide  and  up  to  8  feet  long. 

The  details  of  a  box  skylight  manufactured  by  Vaile  &  Young, 
Baltimore,  Md.,  is  shown  in  Fig.  150. 

Use  of  Window  Shades. — Where  factory  ribbed  glass  is  placed 
so  as  to  throw  light  on  the  ceiling,  screens  or  shades  are  seldom  required, 


3°4 


WINDOWS  AND  SKYUGHTS 


FIG.  150. 

however,  under  ordinary  conditions  shades  are  necessary  when  bright 
sunlight  strikes  the  window.  The  glass  used  in  factory  ribbed  and 
rough  plate  glass  as  made  in  England  is  somewhat  opaque,  and  the 
atmosphere  is  somewhat  hazy,  so  that  the  use  of  shades  in  their  shops 
is  in  most  cases  unnecessary.  The  glass  made  in  this  country  is  so 
clear  and  our  atmosphere  is  so  translucent  that  it  has  been  found  nec- 
essary to  use  shades  where  windows  and  shades  are  exposed  to  direct 
sunlight.  The  most  effective  and  satisfactory  shade  is  a  thin  white  cloth, 
which  cuts  off  about  60  per  cent  of  the  light. 

Size  and  Cost  of  Glass. — The  regular  stock  sizes  of  plane  glass 
varies  from  6  x  16  inches  by  single  inches  up  to  24  x  30  inches,  and  above 
that  by  even  inches  up  to  60  x  70  inches  for  double  strength  glass  and 
30  x  50  inches  for  single  strength  glass. 

The  weights  of  different  thickness  of  glass,  assuming  156  pounds 
as  the  weight  of  one  cubic  foot  of  glass  are  given  in  the  following  table : 
WEIGHT  OF  GLASS  PER  SQUARE  FOOT. 

Thickness— in ya      3-16    %%%%%! 

Weight— Ibs 1.62    2.43  3.25  4.88  6.50  8.13  9.75  13 

The  cost  varies  with  the  quality  and  the  size,  being  about  twice  as 
much  to  glaze  a  given  area  with  30  x  36-inch  lights  as  with  10  x  12- 
inch  lights.  The  discounts  given  from  the  standard  price  list  vary  so 


COST  OF  WINDOWS 


305 


much  that  prices  are  of  very  little  value  except  to  give  an  idea  of  the  rel- 
ative cost  of  different  sizes  of  glass  and  to  serve  as  a  basis  for  estimates. 
In  1903  American  window  glass  was  quoted  about  as  given  in 

Table  XXV. 

TABLE  XXV. 

COST  OF  WINDOW  GLASS  IN  CENTS  PER  SQUARE  FOOT. 


Size  of  Lights 
in  Inches. 

Single  Strength. 

Double  Strength. 

AA 

A 

B 

AA 

A 

B 

10  X  12 

5.1 

4.3 

4.0 

6.8 

6.0 

5.5 

14  X  20 

5.4 

4.5 

4.3 

7.5 

6.6 

6.1 

16  X  24 

5.8 

4.8 

4.5 

8.3 

7.3 

6.7 

20  X  30 

6.0 

5.1 

4.7 

8.9 

7.9 

7.4 

24  X  36 

6.4 

5.5 

4.9 

9.4 

8.3 

7.6 

In  1903  the  different  kinds  of  glass  were  quoted  in  small  quantities 
at  the  factory  about  as  follows: 

Wire  glass  %  inch  thick 23  cents  per  sq.  ft. 

Factory  ribbed  glass  j£  inch  thick 9     "       "      •"    " 

Maze  glass  %  inch  thick 12     "       "      "    " 

Maze  glass  3- 16  inch  thick 18     "       "       "" 

Prismatic  glass  from  25  to  50  cents  per  sq.  ft. 

Re f rax  glass  (sheet  prisms)  made  by  the  Union  Plate  Glass  Co., 
Limited,  Pocket  Nook,  St.  Helens,  England,  was  quoted  in  1903  as 
follows  at  the  factory :  Ordinary  refrax  glass  Y^"  thick  with  5  prisms 
to  the  inch,  cut  to  any  size  up  to  60"  x  90",  20  cents  per  sq.  ft. ;  wired 
refrax  glass  5-16  inch  thick  with  5  prisms  to  the  inch,  cut  to  any  size 
up  to  40"  x  90",  25  cents  per  sq.  ft. 

Maltby  prisms,  made  by  Geo.  K.  Maltby,  Boston  Mass.,  3-16" 
thick  with  6  prisms  to  the  inch  costs  about  25  to  30  cents  per  sq.  ft. 

Cost  of  Windows. — Windows  with  frames  for  mill  buildings  will 
cost  from  15  to  25  cents  per  square  foot,  depending  upon  the  size  and 
quality  of  the  sash,  the  size  of  the  opening,  and  cost  of  glass  and 
frames.  In  1900  the  cost  was  about  16  cents  per  square  foot  for  D.  S. 


306  WINDOWS  AND  SKYLIGHTS 

glass  with  box  frames  and  sash,  and  9  cents  for  S.  S.  glass  with  plank 
frames  and  sash.  In  1900  skylights  cost  from  23  to  30  cents  per  square 
foot  with  D.  S.  glass.  Windows  are  commonly  estimated  at  25  cents 
per  square  foot  and  skylights  at  from  40  to  50  cents  per  square  foot 
in  making  preliminary  estimates. 

The  American  Luxfer  Prism  Company  manufacture  sheet  prisms 
for  factory  purposes  that  can  be  cut  to  fit  any  opening  up  to  36"  x  84". 
The  cost  of  sheet  prisms  to  fit  ordinary  windows  is  about  40  cents 
per  square  foot.  The  improved  skylight  prisms  made  by  this  company 
cost  about  $1.50  per  square  foot. 

TRANSLUCENT  FABRIC.— Translucent  fabric  consists  of  a 
wire  cloth  imbedded  in  a  translucent,  impervious,  elastic  material,  prob- 
ably made  of  linseed  oil.  The  fabric  may  be  bent  double  without  cracking 
and  is  so  elastic  that  changes  due  to  temperature  or  vibrations  do  not  af- 
fect it.  If  a  sheet  of  translucent  fabric  is  suspended  and  a  fire  applied  to 
the  edge,  it  will  burn  up  leaving  a  carbonaceous  covering  on  the  wire. 
But  if  the  edges  are  protected  it  will  burn  only  with  great  difficulty. 
Live  coals  falling  on  skylights  of  this  material  will  char  and  burn  holes 
but  will  not  set  fire  to  the  fabric.  It  is  therefore  practically  fireproof. 

Translucent  fabric  will  not  transmit  as  much  light  as  glass,  but 
makes  a  most  excellent  substitute  therefore.  It  shuts  off  sufficient 
light  so  that  the  lighting  is  uniform  throughout  the  shop  and  makes  it 
possible  for  men  to  work  directly  under  it  without  shading.  Where 
one-quarter  of  the  roof  is  covered  with  the  fabric  the  lighting  is  prac- 
tically perfect.  The  fabric  should  be  washed  with  castile  soap  and 
warm  water  occasionally,  and  should  be  varnished  every  year  or  two 
with  a  special  varnish  furnished  by  the  manufacturers.  It  is  said  to 
become  less  opaque  with  age.  When  properly  cared  for  the  fabric 
has  been  known  to  give  good  service  for  ten  years.  The  fabric  is  man- 
ufactured in  sheets  3'  3"  wide  and  in  lengths  from  4'  6"  to  9'  o". 
The  framework  for  translucent  fabric  is  the  best  made  of  wood.  A 
standard  frame  for  sheets  3'  3"  x  6'  3"  is  shown  in  Fig.  151.  The  fab- 
ric must  be  stretched  tight  and  carefully  nailed  around  the  edges  of 
the  sheet.  The  capped  joint  with  metal  cap  shown  in  Fig.  151  is  very 


COST  OF  TRANSLUCENT  FABRIC 


307 


satisfactory  as  it  holds  the  fabric  tight,  and  will  give  slightly  to  accom- 
modate changes  in  temperature. 

Cost  of  Translucent  Fabric. — The  fabric  costs  from  13  to  15  cents 
per  square  foot  at  the  factory  at  Quincy,  Mass.  The  framework, 
freight  and  cost  of  laying  will  probably  be  as  much  more,  making  the 
entire  cost  of  skylights  from  25  to  30  cents  per  square  foot. 

Translucent  fabric  has  been  quite  widely  used  and  has  given  uni- 
formly good  results.  It  has  been  used  recently  in  the  A.  T.  &  S.  F. 
R.  R.  shops  at  Topeka,  Kas. 


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"~~-Z~*lz'Wood 

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*~-No.  10  Ga/  Wire 

*--^"*/£Wood 

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w~—No.lOGa/.Wre 

4-^"*/?~)V<xx* 

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X" 


Detail  of  Detail  of  Detail  of 

Lap  Joint  Lock  Joint      Copped  Joint 


Method  of  Fastening 
Ends  of  Wire 


FIG.  151. 

Double  Glazing. — The  condensation  on  the  inner  surface  of  glass 
can  be  prevented  by  double  glazing  the  windows  and  skylights.  Build- 
ings with  double  glazing  are  also  very  much  easier  to  heat  than  those 
with  single  glazing,  the  air  space  between  the  sheets  of  glass  acting  as 
an  almost  perfect  non-conductor  of  heat. 

Details  of  Windows  and  Skylights. — The  details  of  window's  in 
use  in  different  sections  of  the  country  vary  a  great  deal  on  account  of 
the  varied  conditions.  In  buildings  that  have  to  be  heated  and  ventil- 
ated through  the  windows  at  the  same  time,  it  is  necessary  to  provide 
some  means  of  opening  and  closing  the  windows  quickly  and  easily; 
while  in  many  other  cases  the  sash  can  remain  fixed.  The  author  would 
call  especial  attention  to  the  saving  in  fuel  by  the  use  of  double  glazing ; 
the  loss  of  heat  through  a  double  glazed  skylight  has  been  shown  by 


3o8 


WINDOWS  AND  SKYUGHTS 


experiment  to  be  only  about  one-half  what  it  is  through  a  single  glazed 
skylight. 

Details  of  windows  for  use  in  ordinary  brick  and  stone  walls  can 
be  found  in  books  on  architectural  construction  and  will  not  be  given 
here.  A  few  of  the  best  designs  available  for  windows  in  buildings 
with  corrugated  steel,  expanded  metal  and  plaster,  and  similar  walls, 
have  been  selected  and  are  given  on  the  following  pages. 

The  different  types  of  windows  for  buildings  covered  with  cor- 
rugated steel  siding  as  used  by  the  American  Bridge  Company  are  shown 
in  Figs.  152  to  156  inclusive. 


Sill 


ELEVATION 


SECTION 


i* W-  G/ass, 

PLAN 

FIG.  152.    DESIGN  FOR  A  CONTINUOUS  FIXED  SASH  WINDOW. 


DETAILS  OF  WINDOWS 


3°9 


The  sash  frames  are  constructed  of  white  pine  and  are  glazed  usu- 
ally with  A  quality  American  glass.  The  common  sizes  of  glass  used  in 
these  windows  are  io"x  12",  12"  x  12",  10"  x  14"  and  12"  x  14"  single 
strength.  For  lights  larger  than  12"  x  14",  double  strength  glass  is 
used.  The  window  shown  in  Fig.  152  is  used  where  light  is  desired 
without  ventilation.  This  detail  is  used  principally  for  monitor  ven- 
tilators or  for  windows  placed  out  of  reach.  Where  it  is  desirable  to 
obtain  ventilation  as  well  as  light  the  window  frame  with  sliding  sash 
shown  in  Fig.  153  is  used. 


ELEVATION 

,-  %  "*2  "-5 fop 


SECTION 


V  V  Rot/net     U  -  W=G/a55.Mur>fyn5  +4j  '-  -H 
PLAN 


FIG.  153.    DESIGN  FOR  WINDOW  FRAME  WITH  SLIDING  SASH. 


3io 


WINDOWS  AND  SKYLIGHTS 


ELEVATION 


SECTION 


-~l~-j.  filour* 


PLAN 
FIG.  154.  DESIGN  ^OR  WINDOW  FRAME  WITH  COUNTERBALANCED  SASH 


Amount  of  Light  Required.  —  The  amount  of  glazed  surface  re- 
quired in  mill  buildings  depends  upon  the  use  to  which  the  building  is 
to  be  put,  the  material  used  in  glazing,  the  location  and  angle  of  the 
windows  and  skylights,  and  the  clearness  of  the  atmosphere.  In  glazing 
windows  for  mills  and  factories  in  which  the  determination  of  color 
is  a  necessary  part  of  the  work,  care  should  be  used  to  obtain  a  clear 
white  glass  for  the  reason  that  the  ordinary  commercial  glass  breaks 
up  the  light  passing  through  it  so  that  the  determination  of  color  is 
difficult. 


AMOUNT  OF  LIGHT  REQUIRED 


311 


Car  5 fee/ 
ELEVATION 


SECTION 


^        >*"*j#'         .'I'  ii 

. .  '       1 1  «i  .1°  ..» 

>•* 
*  -  W-  ^7JJ,  Munftns  +4z  "-  •*{ 

PLAN 
FIG.  155.    DESIGN  FOR  WINDOW  FRAME  WITH  WEIGHTED  SASH. 

It  is  common  to  specify  that  not  less  than  10  per  cent  of  the  ex- 
terior surface  of  ordinary  mill  buildings  and  25  per  cent  of  the  exterior 
surface  of  machine  shops  and  similar  structures  shall  be  glazed.  One- 
half  of  the  glazing  is  usually  required  to  be  in  the  roof  in  the  form  of 
skylights.  With  translucent  fabric  it  has  been  found  that  the  lighting 
is  good  where  25  per  cent  of  the  roof  is  glazed. 

The  present  tendency  in  shop  and  factory  design  is  to  make  ar» 


3I2 


WINDOWS  AND  SKYLIGHTS 


SECTION 


}<  -  {V  = 


PLAN 
FIG.  156.    DESIGN  FOR  WINDOW  FRAME  WITH  SWINGING  SASH. 

much  of  the  side  walls  and  roof  of  glass  as  possible ;  the  danger  of  leak- 
age around  and  through  skylights  has  prevented  many  from  making 
use  of  skylights,  although  with  the  present  methods  of  glazing  there 
is  no  reason  why  any  leakage  should  occur.  The  shops  of  the  Grant 
Tool  Company,  at  Franklin,  Pa.,  shown  in  Fig.  157,  is  a  good  illustra- 
tion of  side  wall  lighting,  while  the  steam  engineering  buildings  for  the 
Brooklyn  Navy  Yard,  described  in  Part  IV,  is  a  good  illustration  of 
side  wall  and  skylight  lighting.  The  A.  T.  &  S.  F.  shops  described 
in  Part  IV,  is  a  good  illustration  of  side  wall,  skylight  and  saw  tooth 
roof  lighting  combined. 

The  Central  Railway  of  New  Jersey  shops  at  Elizabeth,  N.  J., 
have  skylights  made  of  translucent  fabric  in  the  different  buildings  in 


AMOUNT  OF  LIGHT  REQUIRED 


3*3 


Ztty 


1 1 1 '--- V 99?T«n*r  *>  CtnttC 

FlG.  157.     SHOPS  OF  THE  GRANT  TOOL  WORKS,  FRANKLIN,  PA. 

per  cents  of  the  entire  roof  surface  as  follows:  Blacksmith  shop  30 
per  cent ;  machine  shop  36  per  cent ;  and  paint  and  repair  shop  55  per 
cent. 

The  Lackawanna  and  Western  Railway  blacksmith  shop  has  13 
square  feet  of  skylight  per  100  square  feet  of  floor  area. 

In  the  Great  Northern  Railway  shops  at  St.  Paul,  Minn., — Railway 
Gazette,  June  16,  1903 — all  skylights  have  vj-inch  ribbed  glass,  below 
which  is  double  strength  window  glass.  Suitable  drainage  is  provided 
for  the  moisture  which  collects  on  the  upper  surface  of  the  latter.  Wire 
netting  is  stretched  under  the  skylights  to  prevent  broken  glass  from 
falling  into  the  shops.  The  walls  are  supplied  with  windows  set  at  12 
feet  centers,  55  panes  to  each  sash. 

The  skylights  of  the  A.  T.  &  S.  F.  R.  R.  shops  at  Topeka,  Kas., 
are  made  of  translucent  fabric,  about  20  per  cent  of  the  roof  surface 
being  fabric. 

The  skylights  of  the  machine  shop  of  the  Chicago  City  Railway 
are  made  of  wire  glass,  about  35  per  cent  of  the  roof  being  glass. 


WINDOWS  AND  SKYLIGHTS 


The  machine  shop  of  the  Lehigh  Valley  Ry.,  at  Sayre,  Pa.,  will 
have  the  side  windows  of  plane  glass.  The  locomotive  shop  will  have 
factory  ribbed  glass  in  the  side  windows  and  wire  glass  in  the  roof 
and  monitor  skylights. 

About  25  per  cent  of  the  roof  of  the  St.  Louis  Train  Shed  is  sky- 
light. 

In  the  American  Car  and  Foundry  Company's  shop  at  Detroit, 
about  27  per  cent  of  the  exterior  surface  is  ribbed  glass. 

Fully  60  per  cent  of  the  exterior  surface  of  the  Steam  Engineer- 
ing Buildings  for  the  Brooklyn  Navy  Yard  is  of  glass. 


FIG.  I57a.    DETAILS  OF  SAW  TOOTH  WINDOWS  FOR  P.  &  L.  E.  R.  R. 
SHOPS.     SEE  FIG.  84d. 


SKYLIGHTS  FOR  TRAIN  SHEDS  3*5 

Experience  with  Skylight  Construction  for  Railway  Train 
Sheds. — In  1904  a  committee  was  appointed  by  a  prominent  eastern 
trunk  line  to  investigate  and  report  on  train  shed  skylight  failures  and 
their  remedy.  The  committee  examined  the  Broad  Street  Station  train 
shed,  Camden  and  Reading  Terminal  train  sheds,  and  other  structures 
in  Philadelphia;  the  train  shed  at  Jersey  City;  the  North  German 
Lloyd  Steamship  piers  at  Hoboken ;  the  N.  Y.  C.  &  H.  R.  R.  R. 
train  shed,  the  Macey  Building,  and  other  structures  in  New  York; 
the  South  Union,  North  Union,  and  Back  Bay  stations,  and  the 
Charlestown  Navy  Yard  in  Boston;  the  Union  Station,  and  the  Pitts- 
burg  &  Lake  Erie  station  in  Pittsburg;  and  the  Westinghouse  Shops 
in  East  Pittsburg.  A  complete  report  is  printed  in  Engineering  News, 
April  21,  1904. 

The  conclusions  of  the  committee  were  as  follows : 

1.  That  gas  and  smoke  from  locomotives,  because  of  its  influence 
on  the  metal   framework   of  skylights,   is  the  primary  cause  of  the 
breakage  of  glass. 

2.  That  the  contraction  and  expansion  of  the  metal  frame  is 
-also  a  serious  cause  of  breakage  where  the  glass  is  tightly  fitted  in 
the  frames. 

3.  From  the  testimony  elicited  and  from  personal  observations, 
we  find  the  percentage  of  breakage  in  ribbed,  hammered,  and  wire 
glass  is  about  equal.     We  do  not  find  that  the  breakage  of  wire  glass 
results  from  any  internal  stress  being  set  up  by  the  contraction  and 
expansion  of  the  wire  within. 

4.  The  larger  sizes  of  glass  break  more  readily  than  the  smaller. 

5.  Glass   set  horizontally,  or  at  an  angle,  breaks  more   readily 
than  glass  set  vertically. 

6.  Wire  netting  hung  under  glass,  from  the  effect  of  gases  upon 
it,  is  unreliable. 

7.  Wire   glass   is   most   desirable,   because  when   fractured,   the 
wire  will  generally  hold  it  in  position  until  repairs  can  be  made. 

8.  Steel  bars,  such  as  are  used  in  skylights  at  Broad  Street  and 
Jersey  City  train  sheds,  because  of  the  effect  of  the  gases  on  same,  are 
unsatisfactory. 

9.  Wooden  bars,  such  as  are  used  in  skylights  at  the  Jersey  City 
train  shed,  are  desirable,  being  unaffected  by  gases.     We  recommend 
a  zinc  cap  in  the  place  of  the  wooden  cap. 


22 


3*6  WINDOWS  AND  SKYLIGHTS 

10.  We  recommend  that  a  zinc  expansion  bar  be  used  with  brass 
bolts  in  preference  to  wooden  bars.    We  are  led  to  this  conclusion  from 
the  condition  of  the  zinc  cap  on  the  skylights  on  the  Jersey  City  train 
shed,  which  show  no  deterioration  from  effect  of  gas. 

11.  We  recommend  that  the  sizes  of  glass  used  in  skylights  should 
not  exceed  24  X  36  inches. 

12.  We  recommend   for   future  construction  and  present  train 
sheds,  where  same  can  be  adopted,  a  monitor  form  of  skylight,  prefer- 
ably placed  parallel  with  the  tracks,  of  large  dimensions;   set   far 
enough  apart  so  that  one  monitor  will  not  obstruct  the  light  of  an- 
other; small  sizes  of  glass,  set  in  wooden  or  approved  metal  frames, 
frames  set  loose  enough  to  overcome  the  contraction  and  expansion  of 
the  metal  work  of  the  shed. 

13.  We  recommend  ventilating  the  monitors  at  the  top,  the  open- 
ing being  covered  with  an  umbrella  shelter,  also  by  putting  on  each 
side  of  the  monitor  an  opening  under  the  eaves  above  the  glass  the 
entire  length. 


CHAPTER  XXIV. 

VENTILATORS. 

Ventilation. — Mill  buildings  are  ventilated  either  by  forced  draft 
or  by  natural  ventilation.  Natural  ventilation  is  usually  sufficient,  al- 
though forced  ventilation  is  necessary  in  many  factories  and  mills.  The 
problem  of  ventilation  is  too  large  to  consider  fully  in  this  place  and 
the  natural  method  of  ventilation  only  will  be  discussed.  The  amount 
of  air  required  depends  on  the  use  to  which  the  building  is  to  be  put; 
a  common  specification  for  the  ventilation  of  mill  buildings  being  that 
ventilators  shall  be  provided  and  located  so  as  to  ventilate  the  building 
properly,  and  shall  have  a  net  opening  for  each  100  square  feet  of  floor 
space  of  not  less  than  one-fourth  square  foot  for  clean  machine  shops 
and  similar  buildings ;  of  not  less  than  one  square  foot  for  dirty  ma- 
chine shops;  of  not  less  than  four  square  feet  for  mills;  and  not  less 
than  six  square  feet  for  forge  shops,  foundries  and  smelters.  Ventila- 
tors in  high  buildings  are  more  effective  than  in  low  ones.  The  follow- 
ing table  will  give  an  idea  of  the  effect  of  height  on  ventilation.* 
Height  above  ground.  20'  30'  40'  50' 

Machine  shop,  sq.  ft.  per  100     %          Y±          $/§          j£  round  vents. 
Mills,  "     "     "      "      7  6  5  4  Louvre  vents. 

Forge  shops,      «««•«£  g  7  6  Louvres  or 

open  vents. 

Monitor  Ventilators. — The  openings  in  the  clerestory  of  monitors 
are  fitted  with  louvres,  shutters  or  sash,  or  may  be  left  entirely  open. 
Louvres  are  made  in  many  different  ways,  the  Sniffler  Louvres  shown  in 
Fig.  158,  and  the  Berlin  Louvres  shown  in  Fig.  159,  are  in  common  use. 
The  details  of  these  louvres  as  made  by  various  firms  differ  some- 
what. 

*Mill  Building  Construction,  H.  G.  TyrrelL 


3'S 


VENTILATORS 


Roof  5  tee  I  ~- 
Strap- 

Use  angle  upnghts 
at  splice  joints  of  louvres'  ~V^ 


Gauge  of  metal         ~£ 

^y/x>/^<-<     cr**>s~/ //&sJ    **"  -T** 


*^^  unless 
/£"*§" Strap  at  Joints  — •* 

/%7x-  /ength  of  louvres 

7-O",  no  /ap.  Order 

steel  II "wide •  7','6 holes    /If*. 

for  §  "ova/ screw  head    V  ^  :?4| 

^//5  I "  fang  ^-—fe*; 


Roof  S  tee/  - 


FIG.  158.    SHIFFLER  LOUVRES. 


Hoof5re'e/^ 
Clinch  R/Ver^ 


Louvres  made  of  *14 Steel  ^\ 
Max  Length  4 -/i"- End  Lap  T^Wj 
+  "to i"0rder  steel  for /ow-  \!  ^ 
//  "wide  •  /f  "^/Jf5  />?  uprights,  2  ,v^ 
/fc/~^  "<?K7/  screw  head  bolts 
\"/ong- 

l5"Louv/-e 
Flashing  ~~ 


Ftoof  Stee/  -- 


Use  angle  uprights  at 
splice joints  oflowres- 


-_~*_iLou\sre  Block 
/'L^ 


FIG.  159.    BERLIN  LOUVRES. 


The  details  of  the  Shiffler  louvres  shown  in  Fig.  158,  and  of  the 
Berlin  louvres  shown  in  Fig.  159  are  those  adopted  by  the  American 
Bridge  Company.  The  details  of  the  louvres  are  shown  in  the  cuts  and 
need  no  further  explanation. 


MONITOR  VENTILATORS. 


3'9 


j 

•  i 

1 

• 

\ 

*N 

N4 

^ 

i. 

• 

1* 

H"  Flashing 


160.    HINGED  MONITOR  SHUTTER 


Details  of  a  hinged  shutter  are  shown  in  Fig.  160.  The  angle  iron 
frame  is  covered  with  a  corrugated  iron  covering.  The  shutters  are 
made  from  6  to  10  feet  long,  with  two  hinges  for  shutters  8  feet  long 
and  three  hinges  for  shutters  more  than  8  feet  long.  Where  shutters 
are  to  be  glazed  they  are  hung  as  in  Fig.  156.  The  lever  gear  shown 
by  the  dotted  lines  is  used  in  the  better  class  of  structures.  This  device 
can  be  used  where  the  shutters  are  glazed  if  care  is  used  in  operating. 

In  smelters  the  clerestory  of  the  monitor  is  often  left  entirely  open 
or  is  slightly  protected  by  self  acting  shutters.  In  the  latter  case  the 
shutters  are  hinged  at  the  bottom  and  are  connected  at  the  top  with  each 
other  and  with  a  counter-weight  so  that  the  shutter  will  ordinarily  make 


320 


VENTILATORS 


an  angle  of  about  30  degrees  with  the  vertical.  A  wind  or  a  storm  will 
close  the  windward  shutter  and  open  the  leeward  shutter  wider.  The 
eaves  of  the  monitor  are  made  to  project,  so  that  very  little  of  the  storm 
enters. 

Cost. — The  shop  cost  for  louvres  is  ordinarily  about  I  cent  per 
pound.  To  this  must  be  added  the  cost  of  the  sheet  steel  and  the  cost 
of  the  framework  and  details.  In  1900  louvres  without  frames  cost 
about  25  cents  per  square  foot. 

Circular  Ventilators. — Circular  ventilators  are  often  used  for  ven- 
tilating mill  buildings  in  place  of  the  monitors,  and  on  buildings  requir- 
ing a  small  area  for  ventilation.  They  are  made  of  galvanized  iron, 
copper  or  other  sheet  metal,  and  are  usually  placed  along  the  ridge  line 
of  the  roof. 


"STAR"  VENTILATOR 


Globe  Ventilator 


GARRY  VENTILATOR 


Acorn  Ventilator.  BUCKEYE  VENTILATOR. 

FIG.  161.    CIRCULAR  VENTILATORS. 


CIRCULAR  VENTILATORS  321 

There  are  many  styles  of  circular  ventilators  on  the  market,  a  few 
of  which  are  shown  in  Fig.  161.  The  Star  ventilator  made  by  Mer- 
chant &  Co.,  Chicago,  is  quite  often  used  and  is  quite  efficient.  It  is 
made  in  sizes  varying  from  2  to  60  inches.  In  1903  Star  ventilators 
made  of  galvanized  iron  were  quoted  about  as  follows:  12-in.,  $2.00; 
i8-in.,  $6.75 ;  24-in.,  $10.00 ;  4O-in.,  $45.00. 

The  Globe  ventilator  made  by  the  Cincinnati  Corrugating  Com- 
pany, Cincinnati,  Ohio;  the  Garry  ventilator  made  by  the  Garry  Iron 
&  Steel  Roofing  Co.,  Cleveland,  Ohio ;  and  the  Acorn  and  Buckeye  ven- 
tilators made  by  the  Youngstown  Iron  &  Steel  Roofing  Co.,  Youngs- 
town,  Ohio,  are  quite  efficient  and  all  cost  about  the  same  as  the  Star 
except  the  Garry  ventilator,  which  is  cheaper. 

Home-made  circular  ventilators  can  be  made  that  are  quite  as  sat- 
isfactory as  the  patented  ventilators  and  are  much  less  expensive.  In 
1900,  ten  36-inch  circular  ventilators  cost  $12.25  each,  and  two  24- 
inch  circular  ventilators  cost  $9.25  each  in  Minneapolis,  Minn.  The 
cost  of  the  24-inch  ventilators  was  large  on  account  of  the  small  number 
made. 


CHAPTER  XXV. 


DOORS. 


Paneled  Doors. — For  openings  from  2'  o"  x  6'  o"  to  3'  o"  x  9'  o" 

ordinary  stock  paneled  doors  are  commonly  used.  The  stock  doors 
vary  in  width  from  2'  o"  to  3'  o"  by  even  inches  and  in  length  by 
4"  to  6"  up  to  7'  o"  for  2'  o"  doors,  and  9'  o"  for  3'  o"  doors.  Stock 
doors  are  made  i^  and  1^4  inches  thick,  and  are  made  in  three  grades, 
A,  B  and  C ;  the  A  grade  being  first  class,  B  grade  fair  and  C  grade 
very  poor.  Paneled  doors  up  to  7  feet  wide  and  2%  inches  thick  can 
be  obtained  from  most  mills  by  a  special  order. 

Wooden  Doors. — Wooden  doors  are  usually  constructed  of 
matched  pine  sheathing  nailed  to  a  wooden  frame  as  shown  in  Fig.  162 
and  Fig.  163. 


Section  A-A 


-'from 3'fo6 '--  • 


Top  Rq,l 


Swing  Wooden  Doors 

FIG.  162. 


Sliding  Wooden  Door 

FIG.  163. 


DETAILS  OF  DOORS 


323 


Designs  for  wooden  swing  doors  are  shown  in  Fig.  162,  and  for 
a  wooden  sliding  door  in  Fig.  163.  These  doors  are  made  of  white  pine. 
Doors  up  to  four  feet  in  width  should  be  swung  on  hinges ;  wider  doors 
should  be  made  to  slide  on  an  overhead  track  or  should  be  counter- 
balanced and  raise  vertically.  Sliding  doors  should  be  at  least  4  inches 
wider  and  2  inches  higher  than  the  clear  opening. 

"Sandwich"  doors  are  made  by  covering  a  wooden  frame  with  flat 
or  corrugated  steel.  The  wooden  framework  of  these  doors  is  com- 
monly made  of  two  or  more  thicknesses  of  %-inch  dressed  and  matched 
white  pine  sheathing  not  over  4  inches  wide,  laid  diagonally  and  nailed 
with  clinch  nails.  Care  must  be  used  in  handling  sandwich  doors  made 
as  above  or  they  will  warp  out  of  shape.  Corrugated  steel  with  i%- 
inch  corrugations  makes  the  neatest  covering  for  sandwich  doors. 

For  swing  doors  use  hinges  about  as  follows :  For  doors  3'  x  6'  or 
less  use  lo-inch  strap  or  lo-inch  T  hinges;  for  doors  3'  x  6'  to 
3'  x  8'  use  1 6-inch  strap  or  1 6-inch  T  hinges ;  for  doors  3'  x  8'  to  4'  x  10' 
use  24-inch  strap  hinges. 

Steel  Doors. — Details  of  a  steel  lift  door  are  shown  in  Fig.  164. 
This  door  is  counterbalanced  by  weights  and  lifts  upward  between  ver- 

ffMe  for*  'sfee/  cable  for  hot  sting  —^ 

'- 


A/o.  tt  Cor  5  fee/  fas 
tcned  fo  this  jtae  ty 
iron  barr  /}  "*£  'ana  s  niters 
os  shown 


Steel  Lift  Door 

FIG.  164. 


324 


DOORS 


tical  guides.    This  door  was  covered  with  corrugated  steel  with  ij4- 
inch  corrugations  as  described  in  the  cut. 

Details  of  a  steel  sliding  door  are  shown  in  Fig.  165.  This  door  is 
made  to  slide  inside  the  building  and  swing  clear  of  the  columns. 
Where  the  columns  are  so  close  together  that  there  is  not  room  enough 
for  the  door  to  slide  the  entire  length  of  the  opening,  it  should  be 
placed  on  the  outside  of  the  building.  The  track  and  hangers  shown 


-.    //  "x,f  "Trre  /ran  -, 

P"  'Jar  Hangers  J  *4  *  J  <5^/  p^, 
Wheefs  about  5  "d/a.  -*A~"  ) 

1 

JA.                                V           10100  * 

\\ 

j" 

r 

y 

f—^&s** 

Hole  in  girt  fo  which 

) 
T                    / 

6 

^ 

door  may  be  /ocked 

I 

from  fne  inside  -N 

\ 

\ 

^~1 

5" 

.^2 

^ 

t- 

I 

'L 

1 

Corrugated  /ron  To 

tfl 

v< 

^ 

^7, 

*e< 

X 

/ron 

te  secured  to  frame 
frynvet/ng  w/fh  4  " 
risers  /L0~£  Counfer- 

A//n\, 

counter^ 

r 

^/ 
A 

/ 

^/ 

^ 
76 

rr, 

~C/i 

de  and 

i 

j(//?k  on  rhe  oufc/de 

f/arrer?etof) 

£> 

76 

X 

o  cor- 

N 

ruaafed\  // 

•??/ 

7. 

N 

is 

i^k 

^ 

^ 

•t 

y 

Cor.  Iron  - 


^/AA 


•Lock  here  fromwtetafe 


Steel  Sliding  Door 
FIG.  165. 

make  a  very  satisfactory  arrangement ;  however  there  is  a  tendency  for 
the  wheels  to  jump  the  track  unless  the  grooves  in  the  wheels  are 
made  very  deep. 

There  are  quite  a  number  of  patented  devices  on  the  market  for 
hanging  sliding  doors.     The  Wilcox  trolley  door  hanger,  track  and 


COST  OF  DOORS 


325 


bolt  latch  shown  in  Fig.  166,  are  efficient  and  are  quite  generally  used'. 
The  prices  of  the  door  fixtures  shown  in  Fig.  166  are  about  as  follows : 
door  hangers,  $2.25  to  $3.00  per  pair ;  steel  track,  10  to  25  cts.  per  ft. ; 
clips,  15  to  25  cts.  each;  door  latch,  $1.00,  f.  o.  b.  the  factory  at 
Aurora,  111.  Discounts  for  this  and  several  other  well  known  makes 
of  door  fixtures  are  given  each  week  in  the  Iron  Age,  New  York,  and 
the  list  prices  are  given  in  the  manufacturer's  catalogs. 


Wilcox  Trolley  Door  Hanger 


Wilcox  Gravity  Door  Bolt  and  Latch 

FIG.  166. 

Cost  of  Doors. — Stock  panel  doors  cost  $1.50  to  $5.00  each,  depend- 
ing upon  the  grade,  size  and  conditions.  The  details  of  steel  doors 
vary  so  much  that  it  is  necessary  to  make  detailed  estimates  in  each 
case.  The  shop  cost  of  the  framework  is  often  quite  high  and  may 
run  as  high  as  3  or  4  cts.  per  pound.  The  wooden  frames  for  sandwich 
doors  cost  from  20  to  25  cts.  per  square  foot.  The  cost  of  hinges,  bolts, 
etc.,  required  for  doors  can  be  found  by  applying  the  discounts  given  in 
the  Iron  Age  to  the  list  prices  given  in  the  standard  lists  (see  Chanter 
XXVIII). 


CHAPTER  XXVI. 
SHOP  DRAWINGS  AND  RULES.* 

SHOP  DRAWINGS.— The  rules  for  making  shop  drawings  in 
use  by  the  American  Bridge  Company  are  given  in  their  Standards  for 
Structural  Details,  and  are  reprinted  in  part,  in  Roofs  and  Bridgesr 
Part  III,  by  Merriman  and  Jacoby.  The  following  rules  are  essentially 
those  in  common  use  by  bridge  companies,  for  mill  buildings  and  ware- 
houses. 

Make  sheets  for  shop  details  24  by  36  inches,  with  two  border 
lines,  Y*  and  I  inch  from  the  edge,  respectively.  For  mill  details  use 
special  beam  sheets.  The  title  should  come  in  the  lower  right  hand 
corner,  and  should  contain  the  name  of  the  job,  the  contract  number, 
and  the  initials  of  the  draftsman  and  checker. 

Detail  drawings  should  be  made  to  a  scale  of  J4  to  I  inch  to  the 
foot.  Members  should  be  detailed  as  nearly  as  practicable  in  the  po- 
sitions in  which  they  occur  in  the  structure.  Show  all  elevations,  sec- 
tions, and  views  in  their  proper  positions.  Holes  for  field  connections 
should  always  be  blackened.  Members  that  have  been  cut  away  to  show 
a  section,  may  be  either  blackened  or  cross-hatched.  Members,  the 
ends  of  which  are  shown  in  elevation  or  plan,  should  be  neither  black- 
ened nor  cross-hatched.  Holes  for  field  connections  should  be  located 
independently,  and  should  be  tied  to  a  gage  line  of  the  member.  When 
metal  is  to  be  planed,  the  ordered  and  finished  thickness  should  be  given. 

In  making  shop  drawings  for  mill  buildings  two  methods  are  in 
use. 

The  first  method  is  to  make  the  drawing  so  complete  that  templets 
can  be  made  for  each  individual  piece,  separately  on  the  bench. 

The  second  method  is  to  give  on  the  drawings  only  sufficient  di- 
mensions to  locate  the  interior  of  the  members  and  the  position  of  the 

*  For  detailed  instructions  see  Appendix  III. 


ERECTION  PLAN  327 

pieces,  leaving  the  templet-maker  to  work  out  the  details  on  the  laying- 
out  floor. 

The  first  method  is  illustrated  in  Fig.  95  and  the  second  in  Fig. 
96.  In  the  second  method  sufficient  figures  should  be  given  to  proper- 
ly locate  the  main  points  in  the  truss ;  the  interior  pieces  should  be  lo- 
cated by  center-lines  corresponding  to  the  gage  lines  of  the  rivets, 
the  centers  of  gravity  lines  or  the  outside  edges  of  the  pieces,  as  the  case 
may  be.  The  drawings  should  always  indicate  the  number  of  rivets  to 
be  used  in  each  connection,  the  size  of  rivets,  the  usual  rivet  pitch,  and 
the  minimum  pitch  allowed. 

Erection  Plan. — The  erection  plan  should  be  made  very  complete. 
All  the  notes  that  it  is  necessary  for  the  erecter  to  have,  should  be  put 
on  the  erection  plans ;  how  much  of  the  structure  is  to  be  riveted  and 
how  much  bolted,  whether  it  is  to  be  painted  after  erection  or  not, 
whether  the  windows  and  doors  are  to  be  erected  or  not,  etc.  Center 
line  drawings  are  usually  sufficient  for  the  erection  plans.  The  name 
and  the  size  of  the  piece  should  be  given  and  every  piece  should  have  a 
name. 

The  following  method  was  used  by  the  Gillette-Herzog  Mfg.  Co., 
for  mill  buildings,  and  was  very  satisfactory: 

If  the  points  of  the  compass  are  known,  mark  all  pieces  on  the 
north  side  with  the  letter  "N",  those  on  the  south  side  with  the  letter 
"S",  etc.  Mark  girts  N.  G.  I ;  N.  G.  2 ;  etc.  Mark  all  posts  with  a 
different  number,  thus :  N.  P.  I ;  N.  P.  2 ;  etc.  Mark  small  pieces  which 
are  alike  with  the  same  mark;  this  would  usually  include  everything 
except  posts,  trusses  and  girders,  but  in  order  to  follow  the  general 
marking  scheme,  where  pieces  are  alike  on  both  sides  of  a  building, 
change  the  general  letter;  e.  g.  N.  G.  7  would  be  a  girt  on  the  north 
side  and  S.  G.  7  the  same  girt  on  south  side.  Then  in  case  the  north 
and  south  sides  are  alike,  only  an  elevation  of  one  side  need  be  shown, 
and  under  it  a  note  thus:  "Pieces  on  south  side  of  building,  in  cor- 
responding positions  have  the  same  number  as  on  this  side,  but  prefixed 
by  the  letter  "S"  instead  of  the  letter  "N."  Mark  trusses  T.  I ;  T. 
2 ;  etc.  Mark  roof  pieces  R.  I ;  R.  2 ;  etc. 


328  SHOP  DRAWINGS  AND  RULES 

The  above  scheme  will  necessarily  have  to  be  modified  more  or 
less  according  to  circumstances ;  for  example,  where  a  building  has  dif- 
ferent sections  or  divisions  applying  on  the  same  order  number,  in 
which  case  each  section  or  division  should  have  a  distinguishing  letter 
which  should  prefix  the  mark  of  every  piece.  In  such  cases  it  will  per- 
haps be  well  to  omit  other  letters,  such  as  N.,  S.,  etc.,  so  that  the  mark 
will  not  be  too  long  for  easy  marking  on  the  piece.  In  general,  how- 
ever, the  scheme  should  be  followed  of  marking  all  the  large  pieces, 
whether  alike  or  not,  with  a  different  mark.  This  would  refer  to  pieces 
.  which  are  liable  to  be  hauled  immediately  to  their  places  from  the 
cars.  But  for  all  smaller  pieces  which  are  alike,  give  the  same  mark. 

For  architectural  buildings  adopt  the  following  general  scheme  of 
marking:  The  basement  "A";  first  floor  "B"-;  second  floor  "C";  then 
mark  all  the  pieces  on  the  first  floor  B.  I ;  B.  2 ;  etc. ;  columns  between 
first  and  second  floors  B.  C.  I ;  B.  C.  2 ;  etc. 

It  will  greatly  aid  the  detailing,  checking  and  erection  if  small  sec- 
tions are  made  showing  the  principal  connections,  such  as  girt  connec- 
tions, purlin  connections,  etc. 

The  erection  plans  of  a  mill  building  drawn  in  accordance  with 
these  rules  are  shown  in  Fig.  167  and  Fig.  168. 

CHOICE  OF  SECTIONS.— In  designing,  it  will  be  found  eco- 
nomical to  use  minimum  weights  of  sections,  and  to  use  sections  that 
can  be  most  easily  obtained.  As  small  a  number  of  sizes  should  be 
used  as  is  practicable  where  material  is  to  be  ordered  from  the  mill, 
if  good  delivery  is  to  be  expected.  The  ease  with  which  any  section  can 
be  obtained  in  a  mill  order,  depends  upon  the  call  that  that  particular 
mill  is  having  for  the  given  section.  If  there  is  a  large  demand  for 
the  section,  it  will  be  rolled  at  frequent  intervals,  while  if  there  is 
little  or  no  demand  for  the  section,  the  rollings  are  very  infrequent  and 
a  small  order  may  have  to  wait  for  a  long  time  before  enough  orders 
for  the  section  will  accumulate  that  will  warrant  a  special  rolling.  The 
ease  with  which  sections  can  be  obtained  will,  therefore,  depend  upon 
the  mill  and  the  conditions  of  the  market.  The  standard  and  permissible 


CHOICE  OF  SECTIONS 


329 


sizes  of  sections  in  use  by  the  American  Bridge  Company,  are  given  in 

the  following  table. 

Permissible  Angles. 
8"      x  8"  6"      x  $y2" 

5"      x  5"  4"      x  3}/2" 

2}4"  x  2J4"  3J£"  : 

2"        X   2"  3"         X   2 


Standard  Angles. 
6"      x  6"  6"      x  4" 

4"      x  4"  5"      x  3# 

3/2"  x  3/2"  4"      x  3 

3"      x  3"  3X2"  x  3" 

2^2"    X   2^/2"  V         X   2^/2 

2>£"   X   2" 

Standard  Channels. 
15"  8" 

12"  6" 

10" 

Standard  I  Beams. 


Permissible  Channels 

t 


20" 
l8", 
12" 


6" 


10" 

8" 
6" 


H" 


Permissible  I  Beams. 

24" 

? 

Permissible  Tees. 

3"  x  3"  x  y&"  2"  x  2"  x  5-16" 

Permissible  Zee  Bars. 
5"  4"  3" 

Standard  Flats. 

3"  6"  12" 

3/2"  7"  14" 

4"  8" 

4/2"  9" 

5"  10" 

Standard  Rounds. 

H"          H"         i"  ij4"  i. 

Standard   Squares. 


Other  sizes  than  those  specified  may  be  obtained,  but  the  time  of 
delivery  will  be  very  uncertain  unless  the  order  is  large  enough  to  war- 
rant a  rolling. 

Deck  beams,  bulb  angles  and  special  section  Z-bars  are  hard  to 
get  unless  ordered  in  large  quantities.  Flats  y2"  thick  and  under  are  very 
hard  to  get. 

Flats  under  4"  should  be  ordered  by  y2"  variation  in  width  ;  flats 
and  universal  plates  over  4"  should  be  ordered  by  i"  variation  in  width. 


CHAPTER  XXVIL 
PAINTS  AND  PAINTING. 

Corrosion  of  Steel. — If  iron  or  steel  is  left  exposed  to  the  atmos- 
phere it  unites  with  oxygen  and  water  to  form  rust.  Where  the  metal 
is  further  exposed  to  the  action  of  corrosive  gases  the  rate  of  rusting 
is  accelerated,  but  the  action  is  similar  to  that  of  ordinary  rusting.  Rust 
is  a  hydrated  oxide  of  iron,  and  forms  a  porous  coating  on  the  surface 
of  the  metal  that  acts  as  a  carrier  of  oxygen  and  moisture,  thus  pro- 
moting the  action  of  corrosion.  If  nothing  is  done  to  prevent  or  retard 
the  corrosion  of  the  iron  and  steel  used  in  metal  structures,  the  metal 
rapidly  rusts  away  and  the  structure  is  short  lived.  Wrought  iron  is 
affected  by  corrosion  more  than  cast  iron,  and  steel  is  affected  more 
than  wrought  iron. 

The  corrosion  of  iron  and  steel  may  be  prevented  or  retarded  by 
covering  it  with  a  coating  that  is  not  affected  by  the  corroding  agents. 
This  is  very  effectually  accomplished  by  galvanizing;  but  on  account 
of  the  cost  it  is  impracticable  to  use  the  process  for  coating  anything  but 
sheet  steel  and  small  pieces  of  structural  steel.  The  most  common 
methods  of  protecting  iron  and  steel  are  by  means  of  a  coating  of  paint, 
or  by  imbedding  it  in  concrete. 

PAINT. — The  paints  in  use  for  protecting  structural  steel  may 
be  divided  into  oil  paints,  tar  paints,  asphalt  paints,  varnishes,  lacquers, 
and  enamel  paints.  The  last  two  mentioned  are  too  expensive  for 
use  on  a  large  scale  and  will  not  be  considered. 

OIL  PAINTS. — An  oil  paint  consists  of  a  drying  oil  or  varnish 
and  a  pigment,  thoroughly  mixed  together  to  form  a  workable  mixture. 
"A  good  paint  is  one  that  is  readily  applied,  has  good  covering  powers, 


LINSEED  OIL  331 

adheres  well  to  the  metal,  and  is  durable."  The  pigment  should  be 
inert  to  the  metal  to  which  it  is  applied  and  also  to  the  oil  with  which 
it  is  mixed.  Linseed  oil  is  commonly  used  as  the  varnish  or  vehicle 
in  oil  paints,  and  is  unsurpassed  in  durability  by  any  other  drying  oil. 
Pure  linseed  oil  will,  when  applied  to  a  metal  surface,  form  a  trans- 
parent coating  that  offers  considerable  protection  for  a  time,  but  is  soon 
destroyed  by  abrasion  and  the  action  of  the  elements.  To  make  the 
coating  thicker,  harder  and  more  dense,  a  pigment  is  added  to  the  oil. 
An  oil  paint  is  analogous  to  concrete,  the  linseed  oil  and  pigment  in  the 
paint  corresponding  to  the  cement  and  the  aggregate  in  the  concrete. 
The  pigments  used  in  making  oil  paints  for  protecting  metal  may  be 
divided  into  four  groups  as  follows:  (i)  lead;  (2)  zinc;  (3)  iron; 
(4)  carbon. 

Linseed  Oil. — Linseed  oil  is  made  by  crushing  and  pressing  flax- 
seed.  The  oil  contains  some  vegetable  impurities  when  made,  and 
should  be  allowed  to  stand  for  two  or  three  months  to  purify  and  settle 
before  being  used.  In  this  form  the  oil  is  known  as  raw  linseed  oil, 
and  is  ready  for  use.  Raw  linseed  oil  dries  (oxidizes)  very  slowly  and 
for  that  reason  is  not  often  used  in  a  pure  state  for  structural  iron  paint. 
The  rate  of  drying  of  raw  linseed  oil  increases  with  age ;  an  old  oil  be- 
ing very  much  better  for  paint  than  that  which  has  been  but  recently 
extracted.  Raw  linseed  oil  can  be  made  to  dry  more  rapidly  by  the 
addition  of  a  drier  or  by  boiling.  Linseed  oil  dries  by  oxidation  and 
not  by  evaporation,  and  therefore  any  material  that  will  make  it  take 
up  oxygen  more  rapidly  is  a  drier.  A  common  method  of  making  a 
drier  for  linseed  oil  is  to  put  the  linseed  oil  in  a  kettle,  heat  it  to  a  tem- 
perature of  400  to  500  degrees  Fahr.,  and  stir  in  about  four  pounds  of 
red  lead  or  litharge,  or  a  mixture  of  the  two,  to  each  gallon  of  oil. 
This  mixture  is  then  thinned  down  by  adding  enough  linseed  oil  to 
make  four  gallons  for  each  gallon  of  raw  oil  first  put  in  the  kettle.  The 
addition  of  four  gallons  of  this  drier  to  forty  gallons  of  raw  oil  will 
reduce  the  time  of  drying  from  about  five  days  to  twenty-four  hours. 
A  drier  made  in  this  way  costs  more  than  the  pure  linseed  oil,  so  that 
driers  are  very  often  made  by  mixing  lead  or  manganese  oxide  with 
23 


33  2  PAINTS  AND  PAINTING 

rosin  and  turpentine,  benzine,  or  rosin  oil.  These  driers  can  be  made 
for  very  much  less  than  the  price  of  good  linseed  oil,  and  are  used  as 
adulterants ;  the  more  of  the  drier  that  is  put  into  the  paint,  the  quicker  it 
will  dry  and  the  poorer  it  becomes.  Japan  drier  is  often  used  with  raw  oil, 
and  when  this  or  any  other  drier  is  added  to  raw  oil  in  barrels,  the  oil 
is  said  to  be  "boiled  through  the  bung  hole." 

Boiled  linseed  oil  is  made  by  heating  raw  oil,  to  which  a  quantity 
of  red  lead,  litharge,  sugar  of  lead,  etc.,  has  been  added,  to  a  temper- 
ature of  400  to  500  degrees  Fahr.,  or  by  passing  a  current  of  heated  air 
through  the  oil.  Heating  linseed  oil  to  a  temperature  at  which  merely 
a  few  bubbles  rise  to  the  surface  makes  it  dry  more  rapidly  than  the 
unheated  oil ;  however,  if  the  boiling  is  continued  for  more  than  a  few 
hours  the  rate  of  drying  is  decreased  by  the  boiling.  Boiled  linseed  oil 
is  darker  in  color  than  raw  oil,  and  is  much  used  for  outside  paints.  It 
should  dry  in  from  12  to  24  hours  when  spread  out  in  a  thin  film  on 
glass.  Raw  oil  makes  a  stronger  and  better  film  than  boiled  oil,  but 
it  dries  so  slowly  that  it  is  seldom  used  for  outside  work  without  the 
addition  of  a  drier. 

Lead. — White  Lead  (hydrated  carbonate  of  lead — specific  grav- 
ity 6.4)  is  used  for  interior  and  exterior  wood  work.  White  lead  forms 
an  excellent  pigment  on  account  of  its  high  adhesion  and  covering 
power,  but  it  is  easily  darkened  by  exposure  to  corrosive  gases  and 
rapidly  disintegrates  under  these  conditions,  requiring  frequent  re- 
newal. It  does  not  make  a  good  bottom  coat  for  other  paints,  and  if 
it  is  to  be  used  at  all  for  metal  work  it  should  be  used  over  another  paint. 

Red  Lead  (minium;  lead  tetroxide — specific  gravity  8.3)  is  a 
heavy,  red  powder  approximating  in  shade  to  orange ;  is  affected  .by 
acids,  but  when  used  as  a  paint  is  very  stable  in  light  and  under  ex- 
posure to  the  weather.  Red  lead  is  seldom  adulterated,  about  the  only 
substance  used  for  the  purpose  being  red  oxide.  Red  lead  is  prepared 
by  changing  metallic  lead  into  monoxide  litharge,  and  converting  this 
product  into  minium  in  calcining  ovens.  Red  lead  intended  for  paints 
must  be  free  from  metallic  lead.  One  ounce  of  lampblack  added  to  one 
pound  of  red  lead  changes  the  color  to  a  deep  chocolate  and  increases  the 


PIGMENTS  333 

time  of  drying.  This  compound  when  mixed  in  a  thick  paste  will 
keep  30  days  without  hardening. 

Zinc. — Zinc  white  (zinc  oxide — specific  gravity  5.3)  is  a  white 
loose  powder,  devoid  of  smell  or  taste  and  has  a  good  covering  power. 
Zinc  paint  has  a  tendency  to  peel,  and  when  exposed  there  is  a  tendency 
to  form  a  zinc  soap  with  the  oil  which  is  easily  washed  off,  and  it 
therefore  does  not  make  a  good  paint.  However,  when  mixed  with  red 
oxide  of  lead  in  the  proportions  of  I  lead  to  3  zinc,  or  2  lead  to  I  zinc, 
and  ground  with  linseed  oil,  it  makes  a  very  durable  paint  for  metal 
surfaces.  This  paint  dries  very  slowly,  the  zinc  acting  to  delay  harden- 
ing about  the  same  as  lampblack. 

Iron  Oxide. — Iron  oxide  (specific  gravity  5)  is  composed  of 
anhydrous  sesquioxide  (hematite)  and  hydrated  sesquioxide  of  iron 
(iron  rust).  The  anhydrous  oxide  is  the  characteristic  ingredient  of 
this  pigment  and  very  little  of  the  hydrated  oxide  should  be  present. 
Hydrated  sesquioxide  of  iron  is  simply  iron  rust,  and  it  probably  acts 
as  a  carrier  of  oxygen  and  accelerates  corrosion  when  it  is  present  in 
considerable  quantities.  Mixed  with  the  iron  ore  are  various  other  in- 
gredients, such  as  clay,  ocher  and  earthy  materials,  which  often  form 
50  to  75  per  cent  of  the  mass.  Brown  and  dark  red  colors  indicate 
the  anhydrous  oxide  and  are  considered  the  best.  Bright  red,  bright 
purple  and  maroon  tints  are  characteristic  of  hydrated  oxide  and  make 
less  durable  paints  than  the  darker  tints.  Care  should  be  used  in  buying 
iron  oxide  to  see  that  it  is  finely  ground  and  is  free  from  clay  and  ocher. 

Carbon. — The  most  common  forms  of  carbon  in  use  for  paints  are 
lampblack  and  graphite.  Lampblack  (specific  gravity  2.6)  is  a  great 
absorbent  of  linseed  oil  and  makes  an  excellent  pigment.  Graphite 
(blacklead  or  plumbago — specific  gravity  2.4)  is  a  more  or  less  im- 
pure form  of  carbon,  and  when  pure  is  not  affected  by  acids.  Graphite 
does  not  absorb  nor  act  chemically  on  linseed  oil,  so  that  the  varnish 
simply  holds  the  particles  of  pigment  together  in  the  same  manner  as 
the  cement  in  a  concrete.  There  are  two  kinds  of  graphite  in  common 
use  for  paints — the  granular  and  the  flake  graphite.  The  Dixon 
Graphite  Co.,  of  Jersey  City,  uses  a  flake  graphite  combined  with  silica, 


334  PAINTS  AND  PAINTING 

while  the  Detroit  Graphite  Manufacturing  Co.,  uses  a  mineral  ore 
with  a  large  percentage  of  graphitic  carbon  in  granulated  form.  On 
account  of  the  small  specific  gravity  of  the  pigment,  carbon  and  gra- 
phite paints  have  a  very  large  covering  capacity.  The  thickness  of  the 
coat  is,  however,  correspondingly  reduced.  Boiled  linseed  oil  should 
always  be  used  with  carbon  pigments. 

Mixing  the  Paint. — The  pigment  should  be  finely  ground  and 
should  preferably  be  ground  with  the  oil.  The  materials  should  be 
bought  from  reliable  dealers,  and  should  be  mixed  as  wanted.  If  it  is 
not  possible  to  grind  the  paint,  better  results  will  usually  be  obtained 
from  hand  mixed  paints  made  of  first  class  materials  than  from  the 
ordinary  run  of  prepared  paints  that  are  supposed  to  have  been  ground. 
Many  ready  mixed  paints  are  sold  for  less  than  the  price  of  linseed  oil. 
which  makes  it  evident  that  little  if  any  oil  has  been  used  in  the  paint. 
The  paint  should  be  thinned  with  oil,  or  if  necessary  a  small  amount 
of  turpentine  may  be  added ;  however  turpentine  is  an  adulterant  and 
should  be  used  sparingly.  Benzine,  gasoline,  etc.,  should  never  be  used 
in  paints,  as  the  paint  dries  without  oxidizing  and  then  rubs  off  like 
chalk. 

Proportions. — The  proper  proportions  of  pigment  and  oil  required 
to  make  a  good  paint  varies  with  the  different  pigments,  and  the 
methods  of  preparing  the  paint ;  the  heavier  and  the  more  finely  ground 
pigments  require  less  oil  than  the  lighter  or  coarsely  ground  while 
ground  paints  require  less  oil  than  ordinary  mixed  paints.  A  common 
rule  for  mixing  paints  ground  in  oil  is  to  mix  with  each  gallon  of  lin- 
seed oil,  dry  pigment  equal  to  three  to  four  times  the  specific  gravity 
of  the  pigment,  the  weight  of  the  pigment  being  given  in  pounds.  This 
rule  gives  the  following  weights  of  pigment  per  gallon  of  linseed  oil: 
white  lead,  19  to  26  Ibs. ;  red  lead,  25  to  33  Ibs. ;  zinc,  15  to  21  Ibs. ;  iron 
oxide,  15  to  20  Ibs. ;  lampblack,  8  to  10  Ibs. ;  graphite,  8  to  10  Ibs.  The 
weights  of  pigment  used  per  gallon  of  oil  varies  about  as  follows :  red 
lead,  20  to  33  Ibs. ;  iron  oxide,  8  to  25  Ibs. ;  graphite,  3  to  12  Ibs. 

Covering  Capacity. — The  covering  capacity  of  a  paint  depends 
upon  the  uniformity  and  thickness  of  the  coating ;  the  thinner  the  coat- 


COVERING  CAPACITY 


335 


ing  the  larger  the  surface  covered  per  unit  of  paint.  To  obtain  any 
given  thickness  of  paint  therefore  requires  practically  the  same  amount 
of  paint  whatever  its  pigment  may  be.  The  claims  often  urged  in  favor 
of  a  particular  paint  that  it  has  a  large  covering  capacity  may  mean 
nothing  but  that  an  excess  of  oil  has  been  used  in  its  fabrication.  An 
idea  of  the  relative  amounts  of  oil  and  pigment  required,  and  the  cov- 
ering capacity  of  different  paints  may  be  obtained  from  the  following 
table. 

AVERAGE  SURFACE  COVERED  PER  GALLON  OF  PAINT.* 


Paint. 

Volume    of 
oil. 

Lbs. 
of  Pig- 
ment. 

Volume  and 
Weight 
of  Paint. 

Square  Feet. 

1 
Coat. 

2 
Coats. 

350 
375 
375 
300 
350 
310 

Iron  Oxide  (powdered) 
"    "    (ground  in  oil),. 
Red  Lead  (powdered).. 
White  Lead(g'rdinoil). 
Graphite  (ground  in  oil). 
Black   Asphalt  

1  gal 
1     '« 

1     " 
1     " 
1     " 

1     "(turp.) 
1     " 

8.00 
24.75 
22.40 
25.00 
12.50 
17.25 

Gals.  Lbs. 
1.2=16.00 
2.6=32.75 
1.4=30.40 
1.7=33.00 
2.0=20.50 
4.0=30.00 

600 
630 
630 
500 
630 
515 
875 

Linseed  oil  (no  pigment 

Light  structural  work  will  average  about  250  square  feet,  and 
heavy  structural  work  about  150  square  feet  of  surface  per  net  ton  of 
metal. 

It  is  the  common  practice  to  estimate  ^2  gallon  of  paint  for  the 
first  coat  and  $£  gallon  for  the  second  coat  per  ton  of  structural  steel, 
for  average  conditions. 

Applying  the  Paint. — The  paint  should  be  thoroughly  brushed 
out  with  a  round  brush  to  remove  all  the  air.  The  paint  should  be 
mixed  only  as  wanted,  and  should  be  kept  wrell  stirred.  When  it  is 
necessary  to  apply  paint  in  cold  weather,  it  should  be  heated  to  a  tem- 
perature of  130  to  150  degrees  Fahr. ;  paint  should  not  be  put  on  in 
freezing  weather.  Paint  should  not  be  applied  when  the  surface  is 
damp,  or  during  foggy  weather.  The  first  coat  should  be  allowed  to 
stand  for  three  or  four  days,  or  until  thoroughly  dry,  before  applying 


Tencoyd  Handbook,  page  293. 


336  PAINTS  AND  PAINTING 

the  second  coat.  If  the  second  coat  is  applied  before  the  first  coat  has 
dried,  the  drying  of  the  first  coat  will  be  very  much  retarded. 

Cleaning  the  Surface. — Before  applying  the  paint  all  scale,  rust, 
dirt,  grease  and  dead  paint  should  be  removed.  The  metal  may  be 
cleaned  by  pickling  in  an  acid  bath,  by  scraping  and  brushing  with 
wire  brushes,  or  by  means  of  the  sand  blast.  In  the  process  of  pickling 
the  metal  is  dipped  in  an  acid  bath,  which  is  followed  by  a  bath  of  milk 
lime,  and  afterwards  the  metal  is  washed  clean  in  hot  water.  The 
method  is  expensive  and  not  satisfactory  unless  extreme  care  is  used 
in  removing  all  traces  of  the  acid.  Another  objection  to  the  process  is 
that  it  leaves  the  metal  wet  and  allows  rusting  to  begin  before  the  paint 
can  be  applied.  The  most  common  method  of  cleaning  is  by  scraping 
with  wire  brushes  and  chisels.  This  method  is  slow  and  laborious.  The 
method  of  cleaning  by  means  of  a  sand  blast  has  been  used  to  a  limited 
•extent  and  promises  much  for  the  future.  The  average  cost  of  cleaning 
:five  bridges  in  Columbus,  Ohio,  in  1902,  was  3  cts.  per  square  foot  of 
surface  cleaned.*  The  bridges  were  old  and  some  were  badly  rusted. 
The  painters  followed  the  sand  blast  and  covered  the  newly  cleaned 
surface  with  paint  before  the  rust  had  time  to  form. 

Mr.  Lilly  estimates  the  cost  of  cleaning  light  bridge  work  at  the 
shop  with  the  sand  blast  at  $1.75  per  ton,  and  the  cost  of  heavy  bridge 
work  at  $1.00  per  ton.  In.  order  to  remove  the  mill  scale  it  has  been 
recommended  that  rusting  be  allowed  to  start  before  the  sand  blast  is 
used.  One  of  the  advantages  of  the  sand  blast  is  that  it  leaves  the  sur- 
face perfectly  dry,  so  that  the  paint  can  be  applied  before  any  rust  has 
formed. 

Cost  of  Paint. — The  following  costs  of  paints  will  give  an  idea  of 
costs  and  proportions  used  :** 

Oxide  of  Iron  (Prince's  Metallic  Brown).     One  gallon  of  paint. 

6^4  Ibs.  mineral  at  I  cent 6  cts. 

6^4  Ibs.  raw  linseed  oil — 5-6  gallon  at  56  cents 47    ' 

Cost  of  materials  per  gallon  of  paint 53  cts. 

*Sand  Blast  Cleaning  of  Structural   Steel,  -by  G.  W.  Lilly,  Transactions 
A.  Soc.  C.  E.,  Feb.,  1903. 

**Walter  G.  Berg,  Engineering  News,  June  6,  1895. 


COST  OF  PAINTING  337 

Red  Lead  (National  Paint  Co.).    One  gallon  of  paint. 

20  Ibs.  red  lead  at  5  cents $1 .00 

5^2  Ibs.  raw  linseed  oil — 24  gallon  at  56  cents 42 

Cost  of  materials  per  gallon  of  paint $i  .42 

Graphite  Paint  (Dixon's  Graphite).  Five  pounds  of  graphite  paste 
and  I  gallon  of  oil  make  il/2  gallons  of  paint. 

3^4  Ibs.  graphite  paste  at  12  cents 45  cts. 

24  gallon  boiled  linseed  oil  at  59  cents 44     " 

Cost  of  materials  per  gallon  of  paint 89  cts. 

Mr.  A.  H.  Sabin  in  a  paper  read  before  the  American  Society  of 
Civil  Engineers,  June,  1895,  gives  the  following  as  the  minimum  costs 
of  paints :  Iron  Oxide  paint,  6j4  Ibs.  of  oxide  worth  9^  cents ;  6}4 
Ibs.  of  oil  worth  46^  cents;  mixing  in  a  mill,  barrels,  etc.,  5  cents; 
making  the  actual  cost  of  the  paint  60  cents  per  gallon.  The  cost  of  a 
,  gallon  of  pure  lead  paint  using  20  Ibs.  of  red  lead  per  gallon  and  oil 
at  56  cents  per  gallon  will  cost  not  less  than  $1.50  per  gallon. 

Cost  of  Painting. — The  cost  of  applying  the  paint  depends  upon 
the  condition  of  the  surface  to  be  painted,  and  upon  other  conditions.  A 
common  rule  for  ordinary  work  is  that  the  cost  of  painting  is  about 
two  to  three  times  the  cost  of  a  good  quality  of  paint  required  for  the 
job.  The  cost  of  labor  may  not  be  more  than  the  cost  of  the  paint,  and 
may  be  four  or  five  times  as  much.  The  cost  of  painting  light  struc- 
tural work  in  which  considerable  climbing  has  to  be  done  is  very  dif- 
ficult to  estimate.  The  average  cost  of  painting  four  bridges  in  Den- 
ver, Col.,  with  a  finishing  coat  of  Goheen's  Carbonizing,  in  1899,  was 
51  cents  for  paint  and  80  cents  for  labor,  per  ton  of  metal  painted. 

Priming  Coat. — Engineers  are  very  much  divided  as  to  what 
makes  the  best  priming  coat ;  some  specify  a  first  coat  of  pure  linseed 
oil  and  others  a  priming  coat  of  paint.  Linseed  oil  makes  a  transparent 
coating  that  allows  imperfections  in  the  workmanship  and  rusted  spots 
to  be  easily  seen ;  it  is  not  permanent  however,  and  if  the  metal  is  ex- 
posed for  a  long  time  the  oil  will  often  be  entirely  removed  before  the 
second  coat  is  applied.  It  is  also  claimed  that  the  paint  will  not  adhere 


338  PAINTS  AND  PAINTING 

as  well  to  linseed  oil  that  has  weathered  as  to  a  good  paint.  Linseed 
oil  gives  better  results  if  applied  hot  to  the  metal.  Another  advantage 
of  using  oil  as  a  priming  coat  is  that  the  erection  marks  can  be  painted 
over  with  the  oil  without  fear  of  covering  them  up.  Red  lead  paint 
toned  down  with  lampblack  is  probably  used  more  for  a  priming  coat 
than  any  other  paint ;  the  B.  &  O.  R.  R.,  uses  10  ozs.  of  lampblack  to 
every  12  Ibs.  of  red  lead. 

Without  going  further  into  the  controversy  it  would  seem  that 
there  is  very  little  choice  between  linseed  oil  and  a  good  red  lead  paint 
for  a  priming  coat. 

Finishing  Coat. — From  a  careful  study  of  the  question  of  paints, 
it  would  seem  that  for  ordinary  conditions,  the  quality  of  the  materials 
and  workmanship  is  of  more  importance  in  painting  metal  structures 
than  the  particular  pigment  used.  If  the  priming  coat  has  been  prop- 
erly applied  there  is  no  reason  why  any  good  grade  of  paint  composed 
of  pure  linseed  oil  and  a  very  finely  ground,  stable  and  chemically  non- 
injurious  pigment  will  not  make  a  very  satisfactory  finishing  coat. 
Where  the  paint  is  to  be  subjected  to  the  action  of  corrosive  gases  or 
blasts,  however,  there  is  certainly  quite  a  difference  in  the  results  ob- 
tained with  the  different  pigments.  The  graphite  and  asphalt  paints 
appear  to  withstand  the  corroding  action  of  smelter  and  engine  gases 
better  than  red  lead  or  iron  oxide  paints;  while  red  lead  is  probably 
better  under  these  conditions  than  iron  oxide.  Portland  cement  paint 
is  the  only  paint  that  will  withstand  the  action  of  engine  blasts,  and  its 
use  is  now  entirely  in  the  experimental  stage. 

Conclusion. — It  is  urged  against  red  lead  paint,  that  the  oil  and 
the  lead  form  a  lead  soap  which  is  unstable ;  against  iron  oxide  paint, 
that  since  the  paint  contains  more  or  less  iron  rust  it  is  necessarily  a 
promoter  of  rust ;  against  graphite  paint,  that  there  is  not  enough  body 
in  the  pigment  to  make  a  substantial  paint ;  etc.  There  is  more  or  less 
truth  in  all  the  accusations  made  against  the  different  kinds  of  paint, 
if  the  paint  be  bought  ready  mixed,  or  if  made  out  of  poor  materials ; 
however,  with  a  good  pigment  and  pure  linseed  oil,  none  of  the  above 
objections  are  of  weight. 


MISCELLANEOUS  PAINTS  339 

To  obtain  the  best  results  in  painting  metal  structures  therefore, 
proceed  as  follows:  (i)  prepare  the  surface  of  the  metal  by  carefully 
removing  all  dirt,  grease,  mill  scale,  rust,  etc.,  and  give  it  a  priming 
coat  of  pure  linseed  oil  or  a  good  paint — red  lead  seems  to  be  the  most 
used  for  this  purpose;  (2)  after  the  metal  is  in  place  carefully  remove 
all  dirt,  grease,  etc.,  and  apply  the  finishing  coats — preferably  not  less 
than  two  coats — giving  ample  time  for  each  coat  to  dry  before  applying 
the  next.  Painting  should  not  be  done  in  rainy  weather,  or  when  the 
metal  is  damp,  nor  in  cold  weather  unless  special  precautions  are  taken 
to  warm  the  paint.  The  best  results  will  usually  be  obtained  if  the 
materials  are  purchased  in  bulk  from  a  responsible  dealer  and  the  paint 
ground  as  wanted.  Good  results  are  obtained  with  many  of  the  patent 
or  ready  mixed  paints,  but  it  is  not  possible  in  this  place  to  go  into  a 
discussion  of  their  respective  merits. 

ASPHALT  PAINT.— Many  prepared  paints  are  sold  under  the 
name  of  asphalt  that  are  mixtures  of  coal  tar,  or  mineral  asphalt  alone, 
or  combined  with  a  metallic  base,  or  oils.  The  exact  compositions  of  the 
patent  asphalt  paints  are  hard  to  determine.  Black  bridge  paint  made 
by  Edward  Smith  &  Co.,  New  York  City,  contains  asphaltum,  linseed 
oil,  turpentine  and  Kauri  gum.  The  paint  has  a  varnish-like  finish  and 
makes  a  very  satisfactory  paint.  The  black  shades  of  asphalt  paint 
are  the  only  ones  that  should  be  used. 

COAL-TAR  PAINT.— Coal-tar  used  for  painting  iron  work 
should  be  purified  from  all  constituents  of  an  acid  nature ;  for  this  rea- 
son it  is  preferable  to  employ  coal-tar  pitch  and  convert  it  into  paint 
by  solution  in  benzine  or  petroleum.  Tar  paint  should  preferably  be 
applied  while  hot.  Oil  paint  will  not  stick  to  tar,  and  when  repainting 
a  surface  that  has  been  painted  with  tar  it  is  necessary  to  scrape  the 
surface  if  a  good  job  is  desired.  Tar  paint  does  not  become  hard  and 
will  run  in  hot  weather ;  it  is  therefore  not  a  desirable  paint  to  use  for 
many  purposes. 

CEMENT  AND  CEMENT  PAINT.— Experiments  have  shown 
that  a  thin  coating  of  Portland  cement  is  effective  in  preventing  rust ; 
that  a  concrete  to  be  effective  in  preventing  rust  must  be  dense  and 
made  very  wet.  The  steel  must  be  clean  when  imbedded  in  the  concrete. 
There  is  quite  a  difference  of  opinion  as  to  whether  the  metal  should  be 
painted  before  being  imbedded  or  not.  It  is  probably  best  to  paint  the 


340  PAINTS  AND  PAINTING 

metal  if  it  is  not  to  be  imbedded  at  once,  or  is  not  to  be  used  in  con- 
crete-steel construction  where  the  adhesion  of  the  cement  to  the  metal 
is  an  essential  element.  When  the  metal  is  to  be  imbedded  immediately 
it  is  better  not  to  paint  it. 

Portland  Cement  Paint. — A  Portland  cement  paint  has  oeen 
used  on  the  High  St.  viaduct  in  Columbus,  Ohio,  with  good  results. 
The  viaduct  was  exposed  to  the  fumes  and  blasts  from  locomotives,  so 
that  an  ordinary  paint  did  not  last  more  than  six  months  even  on  the 
least  exposed  portions.  The  method  of  mixing  and  applying  the  paint 
is  described  in  Engineering  News, 'April  24th  and  June  5th,  1902, 
as  follows:  "The  surface  of  the  metal  was  thoroughly  cleaned  with 
wire  brushes  and  files — the  bridge  had  been  cleaned  with  a  sand  blast 
the  previous  year.  A  thick  coat  of  Japan  drier  was  then  applied  and 
before  it  had  time  to  dry  a  coating  was  applied  as  follows :  Apply  with 
a  trowel  to  the  minimum  thickness  of  1-16  inch  and  a  maximum  thick- 
ness of  %  inch  (in  extreme  cases  y2  inch)  a  mixture  of  32  Ibs.  Portland 
cement,  12  Ibs.  dry  finely  ground  lead,  4  to  6  Ibs.  boiled  linseed  oil,  2 
to  3  Ibs.  Japan  drier."  After  a  period  of  about  two  years  the  coating 
was  in  almost  perfect  condition  and  the  metal  under  the  coating  was  as 
clean  as  when  painted.  The  cost  of  the  coating  including  the  hand 
cleaning,  materials  and  labor  was  8  cents  per  square  foot. 

While  this  method  of  protecting  metal  is  somewhat  expensive  it 
will  certainly  pay  for  itself  in  many  places  around  smelters  and  shops. 

References  on  Paint  and  Painting. — For  a  more  complete  dis- 
cussion of  the  subject  of  paints  the  reader  should  consult  the  following: 

Iron  Corrosion  by  Louis  E.  Andes. 

The  Painting  and  Sand  Blast  Cleaning  of  Steel  Bridges  and  Via- 
ducts, by  George  W.  Lilly,  Engineering  News,  April  24th,  1902. 

Rustless  Coatings  of  Iron  and  Steel,  by  M.  P.  Wood,  Transactions 
American  Society  of  Mechanical  Engineers,  Vols.  15  and  16. 

Preservation  of  Iron  Structures  Exposed  to  the  Weather,  by  E. 
Gerber,  Transactions  American  Society  of  Civil  Engineers,  May,  1895. 

Painting  Iron  Railway  Bridges,  by  Walter  G.  Berg,  Engineering 
News,  June  6,  1895. 

Paints  and  Varnishes,  by  A.  H.  Sabin,  Association  of  Engineering 
Societies,  February,  1900.  . 

Application  of  Paints,  Varnishes,  and  Enamels  for  the  Protection 
of  Iron  and  Steel  Structures  and  Hydraulic  Work— a  pamphlet  for 
free  distribution  by  Edward  Smith  &  Company,  New  York. 


CHAPTER  XXVIII. 
ESTIMATE  OF  WEIGHT  AND  COST. 

ESTIMATE  OF  WEIGHT.*— The  contract  drawings  for  mill 
buildings  are  usually  general  drawings  about  like  those  in  Fig.  167  and 
Fig.  1 68,  in  which  the  main  members  and  the  outline  of  the  building 
are  shown,  together  with  enough  sketch  details  to  enable  the  detailer 
to  properly  detail  the  work.  In  making  an  estimate  of  weight  from 
general  drawings  it  is  necessary  that  the  estimater  be  familiar  with  the 
style  of  the  details  in  use  at  the  shop,  and  with  the  per  cent  of  the  main 
members  that  it  is  necessary  to  add,  to  provide  for  details  and  get  the 
total  shipping  weight  of  the  structure.  There  are  two  methods  of  al- 
lowing for  details :  ( I )  to  add  the  proper  per  cent  for  details  to  the  weight 
of  each  main  member  in  the  structure,  and  (2)  to  add  a  per  cent  for 
details  to  the  total  weight  of  the  main  members  in  the  structure.  The 
first  method  is  the  safest  one  to  follo\v,  although  the  second  gives  good 
results  when  used  by  an  experienced  man.  '  The  best  way  to  obtain 
data  on  the  per  cents  of  details  of  different  members  in  buildings  and 
other  structures  is  to  make  detailed  estimates  from  the  shop  drawings. 
By  checking  these  data  with  the  actual  shipping  weights,  the  engineer 
will  soon  have  information  that  will  be  invaluable  to  him.  Second 
hand  data  on  estimating  are  of  comparatively  little  value  for  the  rea- 
son that  the  conditions  under  which  they  hold  good  are  rarely  noted, 
and  it  is  better  that  the  novice  work  out  his  own  data  and  depend  on 
his  own  resources,  at  least  until  he  has  developed  his  estimating  sense. 
In  short  the  only  way  to  learn  to  estimate,  is  to  estimate. 

The  method  of  making  estimates  will  be  illustrated  by  making  an 
estimate  from  the  working  drawings  of  a  steel  transformer  building, 
the  general  plans  of  which  are  shown  in  Figs.  167  and  168.  The 

*  Also  see  Appendix  III. 


342 


ESTIMATE  OF  WEIGHT  AND  COST 


members  marked  "Main  Members"  are  those  given  on  the  general 
drawing,  and  the  "Details"  are  those  members  whose  sizes  are  supplied 
by  the  detailer.  The  building  is  a  steel  frame  building,  60'  o"  wide,  80' 
o"  long,  20'  o"  posts,  pitch  of  roof  J4,  and  is  covered  with  corrugated 


Holes  ft,' 

"S 

A 

/6'-0- 

^^-o• 

SECTION 


L-J.J 


Bracing  in  Plane  of  BoTtom  Chord     Bracing  in  Plane  of  Top  Chord 

FIG.  167.    CROSS-SECTION  AND  PLAN  OF  STEEL  TRANSFORMER  BUILDING. 


ESTIMATE  OF  WEIGHT 


343 


steel.  The  general  plans  of  the  framework  are  shown  in  Figs,  167  and 
1 68,  and  the  plans  and  details  of  the  corrugated  steel  are  shown  in  Figs. 
128  and  129. 

The  weights  of  the  different  sections  were  obtained  from  Cam- 
bria Steel.    The  estimate  is  self  explanatory. 

*—/=>ur/in 


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END  ELEVATION 
FIG.  168.  SIDE  AND  END  ELEVATIONS  OF  STEEL  TRANSFORMER  BUILDING. 


344 


ESTIMATE  OF  WEIGHT  AND  COST 


ESTIMATE   OF    WEIGHT 

Steel  Frame  Transformer  Building  ,  60-0"  Wide  ,  80-0" Long  ,20-0" 
Posts. Pi'rch  of  Roof  3  •  Covered  with  Corrugated  Iron. 


number 
Of 

Pieces 

Shape 

Section 

Length 

Weight 
per 
Foot 

Weic 

ht 

Details 
PerCent 
of  Main 
Members 

Total 
Weight 

Feet 

Inches 

Main 

Members 

Details 

4  Trusses  each  thus: 

4 

is 

32*22x1 

19 

5fc 

6.0 

463 

4 

LS 

18 

0  jfe 

4-9 

353 

4 

is 

3  x  22X  | 

II 

1 

5-0 

2ZE 

4 

i? 

3  x  2  x  ii6 

10 

IO 

4-0 

173 

t 

Is 

3x   2  «1 

16 

2 

4.O 

259 

8 

If 

2*2x4- 

2 

9 

3-2 

70 

4 

is 

3 

IO 

3-6 

84 

8 

If 

2x2x4 

5 

1 

32 

130 

4 

If 

3x2x4 

IO 

5* 

4.0 

167 

4 

L? 

2|  x  £  x  4 

II 

IO 

3-6 

170 

8 

L? 

2x2x4 

10 

9 

32 

271 

1 

L 

3X  2  X4 

19 

2 

4.0 

77 

4 

If 

2X2x4 

6 

0 

3.E 

77 

5 

Is 

2  *  2x4 

5 

7| 

32 

90 

2 

L? 

2x2x4 

4 

3-2 

29 

4 

LS 

3x2  x4 

II 

4 

32 

186 

2 

PIS. 

'8*  ^ 

2 

9/3 

89 

2 

P/s 

7x4 

^i 

595 

7 

2 

PI3 

44x4 

3-61 

6 

6 

Pis 

7x  J. 

1 

o" 

5-95 

36 

II 

Pis 

74x4 

34 

616 

42 

4 

Pis 

85  x  - 

1 

0 

722 

£9 

2 

Pis 

8^x4 

1 

2 

7Z2 

1  7 

4 

PIS 

12  x^ 

I 

10 

iaz 

73 

2 

Pis 

164x4 

l 

8 

1381 

46 

1 

Pis 

24x4 

3 

2 

204- 

65 

4 

PIS 

2x| 

1 

5Z 

255 

15 

12 

PIS 

6i*4 

7 

555 

4Z 

2 

Pis 

92xJ- 

7 

818 

9 

2 

P»s 

54x4 

1 

0 

4.46 

9 

2 

L? 

2|x2  2  x  ^ 

9- 

4:0 

6 

16 

Ls 

3i"2ix  ^ 

7* 

4-9 

45 

2 

L? 

3g  x  2£  x  1 

3| 

4.9 

3 

1348 

5  Rivet  Heads 

Per 

100 

395 

134 

36 

8  Washers 

Per 

100 

30.0 





2621 

684 

24.6 

Total  Weight  of  -4  Trusses  -  3505  X4  = 

14020 

8  Posts  each  thus:- 

4 

[5 

3i  *2i*;i 

19 

H| 

4-9 

3*9' 

1 

PI 

10^x4 

2 

0 

871 

16 

4 

Is 

3i*2i*4 

74 

5-9 

15 

1 

PI 

13x4 

1 

11.05 

13 

1 

PI 

I0x| 

f 

I.I2 

21-25 

41 

2 

LS 

6x3^  x  -J 

IO 

11.6 

19 

2 

L? 

6x4  x  r 

gj 

12-3 

21 

17 

Bars 

2x4 

1 

7£ 

1-7 

47 

160 

f  Rivet  Heads 

Per 

too 

9-95 

16 

39T 

188 

48.1 

Total    Weight  of  8  Posts 

=  579  X  8  = 

463Z 

18652 

ESTIMATE  OF  WEIGHT 


345 


Number 
of 
Pieces 

Shape 

Section 

Length 

Weight 
per 
Foot 

Weiqht 

Details  in 
PerCent 
of  Main 

Members 

Total 
Weight 

Feet 

Inches 

Mam 

Member 

Details 

4     Posts  '.each  thus  :- 

Brought  forward  18652 

I 

I 

9'@  21* 

35 

z\ 

21 

740 

8 

L* 

3l  *3|  x  •* 

5i 

7-1 

26 

Z 

Z 

I? 

6X4X3; 

9 

12.3 

11.6 

13 
17 

PI 

»£§*? 

i 

5 

19-13 

27 

88 

1"  Rivet  Heads 

per  100 

3.93 



9 

Total  Weight  4  PC 

>sts  = 

S37X^ 

740 

-        = 

92 

12-5 

3328 

4    Posts,  each  thus  :- 

i 

I 

9"@     21* 

27 

10i 

Z\ 

586 

6 

I* 

3a  x3|  x  ^ 

5k 

7.1 

20 

1 

L 

6  x  6  x  | 

9 

143 

II 

2 

L« 

6  x  -4  x  2 

62 

12.3 

13 

2 
1 

80 

R 

*»4»] 

9x|8 
i"  Rivet  Heads 

1 

per  100 

9 
5 

11.6 

ISO 
995 

17 

^^ 

586 

96 

'l6.4 

Total  Weight 

4    Posts  =  682  x  4 

= 

2728 

4  Posts,  each  thus;- 

i 

L 

6x6x| 

20 

B\ 

143 

306 

IO 

Rs 

7*i 

62 

595 

33 

1 

PI 

5*4 

9i 

425 

3 

1 

PI 

10x5 

10 

21-25 

18 

1 

L 

5  x  3i  x  S. 

1 

1 

8-7 

9 

3 

L? 

5  x  3j  x  *A 

8 

87 

17 

| 

L 

3zx3ix? 

3 

7-1 

3 

2 

|_S 

6x3f  x| 

si 

116 

18 

100 

|"  River  Heads  per  lOO 

995 

IO 

I 

306 

II  1 

36.3 

Total  Weight  4  Posts  =417*4 

= 

1668 

4   End  Rafters  .each  th'us:- 

I 

C 

7@    9j* 

37 

4 

9.75 

365 

Con  L5  and  Pis 

19 

365 

79 

Z2-0 

Total   Weight  4  End  Rafters  =  4 

44X4 

= 

1776 

2    Eave  Struts,  each  thus-— 

5 

B 

9  e  is4             16 

0 

1325 

1060 

Total  Weight  2  Eave  Struts  =  /6eox£ 

= 

2120 

Bottom  Chord  Bracing  :- 

8 

LS 

3*3  x^; 

18 

0 

4.9 

706 

10 

Is 

7"@I5* 

15 

2 

15.0 

2275 

36 

0 

6  x-4  x  | 

5 

12.3 

184 

4 

15 

3  x  3-x^ 

5 

4.9 

8 

123 

|"Rivet  Heads  per  160 
1 

995 

Z98I 

13 
Z05 

7.0 

Total  Weight  Bottom  Chord  Brocincj  = 

3186 

Purlins  :- 

30 

(s 

5@  62* 

32 

74- 

6.5 

6355 

| 

„ 

15 

Ill 

6-5 

1452 

6 

s 

D 

16 

y| 

65 

650 

6 

L? 

5x3x5 

32 

7| 

82- 

1604 

z 

I* 

15 

8-2 

262 

2 

LS 

" 

16 

7j 

62 

272 

10595 

Total   Weig 

Ht  of  Purlins    = 

44053 

346 


ESTIMATE  OF  WEIGHT  AND  COST 


•lumber! 
of       Shape 
Pieces  1 

Section 

Lenqth 

Weiqht- 
Per 
Foot 

Weight- 

Details  m 

Percent 
of  Mom 

Members 

Total 
Weia.KV 

Feet 

Inches 

Main 

Members 

Details 

Girts  :- 

drouqht 

Forwarc 

A4053 

L> 

A-'  @   5%* 

1664 

linft. 

5.25 

8736 

\J> 

3"x3"x^;" 

96 

.      , 

4.9 

470 

LS 

2  4  "x  2V*2£ 

96 

. 

40 

384 

Total   Weiqht 

9590 

Rods  — 

6 

Rode. 

Z'    0 

28 

0 

2.0 

448 

»6 

Rods 

a"  0 

18 

0 

2.0 

576 

16 

Rods 

15     * 

23 

0 

2.0 

736 

32 

Bolts 

Anchor  §"0 

I 

6 

2.0 

96 

4 

„ 

i.             •• 

\ 

0 

2.0 

8 

18 

Rods 

Louvre    §  0 

3 

0 

\.o 

54 

18 

BolH 

U     |"     0 

1.5 

9 

18 

Sprmq  Cotcnes 

0.5 

9 

36 

Pis 

Anchor  A"X  S" 

4 

1-4 

50 

56 

P.ns 

Cotter  l|"xZ%" 

13 

74 

i  ~7/iv  r\~ 

300 

\7.0 

Toto\  Weiqht 

2060 

Total     Weight 

Steel 

Frame 

worK 

55703 

Corrugated      Iron.-^ 

64-     Squares   No  22  as  pe«-  list,  per   sa.       138 

11592 

70                                  24     ...                  .\M 

7770 

Ridqe  Roll             22    Black 

250 

Fla&inq               22 

414 

Cornice                  20 

1500 

Louvres                 20  and  No  16 

2100 

19362 

4264 

Total    Weiqht     Cor-ruqated     Iron            23626 

Total   Weight 

Steel 

79329 

Summary  — 

Trusses 

II28A 

2736 

Z4-.6 

14020 

4L  Posts 

3128 

1504 

48.1 

4632 

IB        . 

5304 

752 

14.1 

6056 

L. 

•  224 

444 

36.3 

I66& 

End  Rafters 

1460 

316 

?2.0 

1776 

Eave  Struts 

2I2O 

00 

2120 

Bottom  Chord  Brac«nq 

2981 

2*05 

7.0 

3186 

Rods 

1760 

300 

17.0 

2060 

Weicjrct    Excluding     Purlins  ond   6>r+s 

29261 

6257 

220 

35518 

Purlms 

10595 

10595 

G.rts. 

9590 

9590 

Total     Frame  wo  rK 

49446 

6257 

13.0 

55703 

Corrucjated     Iron 

23626 

Total    Weiqht 

79329 

The  weights  and  per  cents  of  three  other  buildings,  are  shown  in 
Table  XXVI.  The  estimates  for  these  buildings  were  made  from  the 
shop  drawings,  and  were  checked  with  the  shipping  weights.  These 
buildings  are  of  light  construction  with  end  post  bents,  (a)  Fig.  i. 


ESTIMATE  OF  COST  OF  Miu,  BUILDING 


347 


ESTIMATE  OF  COST 


Classification  of  Material 

COST  of  Material 

Cost  of  Labor 

WeiqhT 

Price 

Amount 

Price 

Amount 

Riveted  Trusses 

I402O 

<*i.60 

^24.3£ 

•too 

*I4Q2O 

Latticed   Columns 

4632 

1-60 

74.1  1 

1.00 

46u52 

I   Beam 

6056 

1-65 

99-92 

•50 

3026 

L                          " 

J668 

1-60 

2669 

•5O 

834 

C  Struts 

3896 

1-60 

62.34 

2$ 

9-14 

I  Beam    Bracing 

£480 

1-63 

40-9Z 

.25 

6-20 

L  Bracing 

706 

1-60 

11-30 

25 

1-77 

C  Purlins 

10595 

J-60 

169-52 

•15 

15-90 

C  Girts 

9590 

I-6O 

15344 

.15 

14-39 

Rods 

2060 

1-80 

37.08 

1-00 

20.60 

Corrugated  Iron  NO-  £2 

II  592 

Z-60 

301.39 

n                     >>         »    t+ 

7770 

2-70 

209-79 

Ridge  Rol  1,  Louvres,  Etc- 

4264 

2-50 

106-60 

1-00 

41.64 

Asbestos  Mill  Ooard 

1760 

2-50 

44.00 

Poultry  Netting 

4-00 

32-50 

6-d  Barbed  Roofing  Naite 

32 

3.00 

.96 

40-d    Wire  Noils 

5 

2-50 

.13 

540  Stove  Bolts  -36''x  I"  (per  IOC 

0              5 

36-00 

1-94 

5^-0  Washers   l"x£'x.4' 

76 

6-00 

4-56 

Mo  Cut  Washers  3" 

2 

7.00 

.14 

80O   Wire  Staples 

5 

4.00 

-20 

Copper  Rivets  *8-J"long 
(ZOO  Carriage  Bolts  2  x£i"(  per 

6 
100)     ZIO 

25.00 
*I-IO 

1  50 
13-ZO 

200                    "                I"x32"        "               46 

*l.50 

300 

260  Wood  Screws  *i4-g"      •»             10 

*   60 

1.56 

54   Steel  Butts  3i"x32" 

60 

«&00 

4.32 

4-  Mortise  Door    Locks 

10 

75-00 

3-00 

18     10'  T  Hinges 

40 

JZ.OO 

2.16 

a-  10"   Foof  Bolts 

5 

50.00 

/.oo 

2-  Chain  Bolts 

5 

50.00 

100 

96  Window  Weights 

1440 

2.00 

28-60 

24        '.          Locks 

16 

/5-OO 

3^>0 

24        ••          Lffts 

IO 

10.00 

240 

675  Lin.  Ft  Sash  Cord 

30 

15^)0 

4.50 

2-8  Light  Windows  V  Frame 

80 

*  4.00 

8-OO 

12-24-     »            ••                    •• 

/600 

*  5.00 

96X)0 

2   Doors 

800 

*I5-00 

30.00 

2    Doors 

200 

*4-.OO 

+    8-00 

Total  Weic 

ht  87212 

Cost  MaT'1,181  3.89 

Cost  Labor*336.38 

SUMMARY 

Cost  of  Material 

9  IB  13.89 

Cost  of  Shop  Labor 

| 

336-38 

Cost  of  Details 

30  tons   @  3.60 

\OQJOQ 

Cost  of  Shop  Pointing 
Total  Shop  Cost 

40-00 
2398-27 

Freight,  Mill  +05hop 

30  tons    ©  *5-00 

150.00 

Freight,  Shop  to  Site 
Erection,  Structural 

9)         Corrugated 

44   »         @*I6.00 
30  tons    @>*8.OO 
60  sgs.  Roofing  < 
60   »    Siding   ^ 

704.00 
t               240^0 
3?«5            7  MO 
?*.75           45.00 

«          Miscellaneous 

saoo 

_  ,           f  76  gals.  Paint 
Pointmgj  Lo^Qr 

76OO 
1500 

Total  Cost 

*38I3.27 

24 


348 


ESTIMATE  OF  WEIGHT  AND  COST 


TABLE  XXVI. 
WEIGHTS  AND  PER  CENTS  OF  DETAILS  OF  MILL  BUILDINGS. 


5teel   Mill    Buildings    with    Self  Supporting    Frames    covered 
or»    Roof  and    Sides   w\th  one  "thickness  of  Corruqated  Iron, 

Part 
of 
Structure 

40-0'x4frOx  14-0' 
2  Trusses  40-0" 
Pitch  £ 
End  Framinq 

<•""«£££ 

Z  CircularVenlilator 

40  -0*x  46-0"  x  14-0' 
2Trusses  40'-0" 
Pi+chj^ 
End  Framing 

fr-HSfe 

SGrcutar  Ventilator 

60-oV?5-0"xl8-o' 
4  Trusses  60-0 
Pitch  -^ 
End  Framinq 
r   ^       (Rbof*22 

CoCfcon^ufertM- 

3  Circular  Ventilator 

60:OV  80-0"  x  20-0" 
4  Trusses  60-0* 
Pitch  ^ 
End  Framinq 
.      ,       (Roof*  22 
Cor.  Iron  )S)des*24 

Monitor  Ventilators 

Weight 

Details  in 
per  cent 
of  Main 
Members 

Weiqht 

Details  in 
per  cent 
of  Main 
Members 

Weiqht 

Detail  sin 
per  cent 
of  Main 
Members 

Weiqht 

Details  in 
per  cent 
of  Main 
Members 

IBs 

percent 

Ibs. 

per  cent 

Ibs. 

percent 

Ibs 

percent 

Trusses 
A-\-  Columns 
I  Beam     . 
l_  Columns 
End  Rafters 
Eave  Struts 
LowerChord  Bracing 
Rods 
Purlins 
Girts 

2848 
1428 

1146 

912 
1036 
900 
930 
900 
2281 
3170 

25 
.70 
15 
36 
17  . 
0 
22 
15 
5 
2 

2848 
1428 
1146 
952 
1076 
1080 
1049 
920 
3516 
5252 

25 
70 
15 
36 
22 
0 
20 
17 
7 
2 

13940 
3476 
4251 
1470 
3314 
3117 
2763 
1737 
6713 
9895 

344 
52.5 
33.0 
14.0 
11.6 
33.2 
9.7 
6.2 
47 
10.0 

14020 
4632 
6056 
1668 
1776 
2120 
3186 
2060 
\0595 
9590 

24.6 
484 
14.1 
36.3 
200 
0.0 
7.0 
110 
0.0 
00 

Weight  of  FrameworK 
Weiqht  per  Sq.Ft 

15553 
9.8 

19 

17269 
9.0 

20 

50676 
11.2. 

24.0 

55703 
11.7 

130 

Corruqoted  Iron 

5880 

6892 

17000 

23626 

Total  of  Steel 

WeiqhtperSq.Ft. 

ZI453 
13.4 

£4161 

12.6 

67676 
15.1 

79329 
16.5 

Channel  eave  struts  were  used  in  all  except  the  third  building  in  which 
4-angle  laced  struts  were  used.  A  very  good  idea  of  the  per  cent  of 
details  in  the  different  parts  of  the  structures  can  be  obtained  from 
Table  XXVI.  The  details  of  riveted  mill  building  trusses  will  commonly 
vary  between  the  limits  of  25  and  35  per  cent  as  given  in  the  table; 
being  more  often  near  25  than  35  per  cent.  The  per  cents  of  details  in 
trusses  is  practically  independent  of  the  length  of  span,  and  is  larger  for 
light  than  for  heavy  work.  It  should  be  noted  that  the  details  in 
columns  is  mostly  due  to  the  bases  and  connections — the  per  cents  of 
details  will  therefore  decrease  as  the  length  of  the  column  increases. 
The  weights  of  the  other  parts  are  so  variable  that  no  general  rules  can 
be  given.  Where  a  uniform  per  cent  is  added  to  the  total  weight  of 
main  members  to  provide  for  details,  it  is  common  to  add  about  30 


ESTIMATE  OF  COST  349 

per  cent  to  the  weight  of  the  framework  exclusive  of  the  purlins  and 
girts  where  end  bent  (b)  Fig.  I,  is  used.  In  the  estimate  given  it  will 
be  seen  that  the  per  cent  is  only  22,  the  small  value  being  due  in  part 
to  the  use  of  channel  eave  struts  and  the  end  post  framing. 

In  estimating  the  weight  of  corrugated  steel  add  25  per  cent  for 
laps  where  two  corrugations  side  lap  and  6  inches  end  lap  are  required, 
and  15  per  cent  where  one  corrugation  side  lap  and  4  inches  end  lap  are 
required. 

The  weights  of  the  sections,  rods,  bolts,  turnbuckles,  etc.,  are  ob- 
tained from  Cambria  Steel,  or  other  handbook. 

The  engineer  should  use  every  care  to  check  his  work  in  making 
estimates,  the  material  should  be  checked  off  the  drawings,  and  the  cal- 
culations should  be  carefully  checked  and  rechecked.  Slide  rules  and 
adding  machines  are  invaluable  in  this  work.  No  results  should,  how- 
ever, be  allowed  to  pass  until  they  have  been  roughly  checked  by  the 
engineer  by  aliquot  parts,  or  by  making  a  mental  estimate  of  each 
quantity.  The  engineer  can  soon  develop  a  sense  of  estimate,  so  to 
speak,  and  will  often  detect  blunders  intuitively.  Accuracy  is  of  more 
value  in  estimating  than  precision.  While  the  method  outlined  may 
seem  somewhat  crude  at  first  glance,  it  is  nevertheless  true  that  a  pre- 
liminary estimate  made  by  a  skilled  man  will  commonly  be  within  I  or  2 
per  cent  of  the  shipping  weight,  and  if  off  more  than  2^2  per  cent  it  is 
pretty  certain  that  there  was  something  wrong  either  with  the  estimate 
or  with  the  estimater.  The  estimated  weight  should  be  a  little  heavy 
rather  than  light,  say  I  to  2  per  cent. 

ESTIMATE  OF  COST.— The  cost  of  the  different  parts  of  a 
mill  building  varies  with  the  local  conditions,  cost  of  labor,  and  cost 
of  materials.  The  discussion  of  this  subject  will  be  divided  into  (i) 
cost  of  material,  (2)  cost  of  shop  work,  and  (3)  cost  of  erection.  The 
cost  of  transportation  must  also  be  included  in  arriving  at  the  total  cost. 
The  subject  of  costs  is  a  very  difficult  one  to  handle  and  the  author 
would  caution  the  reader  to  use  the  data  given  on  the  following  pages 
with  care,  for  the  reason  that  costs  are  always  relative  and  what  may 


350  ESTIMATE;  OF  WEIGHT  AND  COST 

be  a  fair  cost  in  one  case  may  be  sadly  in  error  in  another  case  which 
appears  an  exact  parallel.  The  price  of  labor  will  be  given  in  each  case, 
or  the  costs  will  be  based  on  a  charge  of  40  cents  per  hour  which  in- 
cludes labor,  cost  of  management,  tools,  etc. 

Cost  of  Material. — The  cost  of  structural  steel  can  be  obtained 
from  the  current  numbers  of  the  Iron  Age,  Engineering  News,  etc.,  or 
may  be  obtained  direct  from  the  manufacturers  or  dealers.  In  1903 
beams,  channels,  angles,  plates,  and  bars  were  quoted  at  about  1.60 
cents  per  pound  f.  o.  b.  Pittsburg.  Beams  18,  20  and  24  inches  deep 
take  o.io  cents  per  pound  higher  price  than  the  base  price  for  beams. 
The  mills  at  present  quote  a  delivered  price  only,  equal  to  the  mill  price 
plus  the  usual  freight  charge.  This  price  is  often  more  than  the  cus- 
tomer could  obtain  by  paying  the  freight  himself,  on  account  of  the 
freight  rebates  that  are  often  allowed. 

Cost  of  Mill  Details.* — Mills  are  allowed  a  variation  in  length  of 
sections  of  J4  of  an  inch ;  which  means  that  beams,  channels,  etc.,  may 
come  y%  of  an  inch  shorter  or  y%  of  an  inch  longer  than  the  length 
called  for.  When  a  less  variation  than  this  is  required  a  special  price 
is  charged  for  cutting  to  exact  length.  The  following  list  of  mill  ex- 
tras adopted  January,  1902,  is  now  in  force : 

LIST  OF  EXTRAS  TO  BE  ADDED  TO  PRICE  OF  PLAIN  BEAMS  AND  CHANNELS. 

1.  For  cutting  to  length  with  less  variation 

than  plus  or  minus  y%  inch $o.  15 

2.  Plain  punching  one  size  hole  in  web  only  .  1 5 

3.  Plain  punching  one  size  hole  in  one  or  both 
flanges .15 

4.  Plain  punching  one  size  hole  in  either  web 

and  one  flange  or  web  and  both  flanges  .25 

5.  Plain  punching  each  additional  size  hole  in 
either  web  or  flange,  web  and  one  flange 

or  web  and  both  flanges .25 

6.  Plain  punching  one  size  hole  in  flange  and 
another  size  hole  in  web  of  the  same  beam 

or  channel .4° 

7.  Punching  and  assembling  into  girders ....  .35 

*  See  Appendix  III. 


COST  OF  MILL  DETAILS  35 ! 

8.  Coping,  ordinary  beveling,  including  cut- 
ting  to    exact    length,    with   or    without 
punching,  including  the  riveting  or  bolting 

of  standard  connection  angles .35 

9.  For    painting    or    oiling    one    coat    with 
ordinary  oil  or  paint .  10 

10.  Cambering    Beams    and    Channels    and 

other  shapes  for  ships  or  other  purposes .  .  .25 

1 1 .  Bending  or  other  unusual  work Shop  rates 

12.  For  fittings,   whether  loose  or  attached, 
such  as  angle  connections,  bolts  and  sepa- 
rators, tie-rods,  etc 1 . 55 

The  above  prices  are  per  100  Ibs.  of  steel. 

In  ordering  material  from  the  mill  the  following  items  should  be 
borne  in  mind.  Where  beams  butt  at  each  end  against  some  other 
member,  order  the  beams  ^  inch  shorter  than  the  figured  lengths ;  this 
will  allow  a  clearance  of  %  inch  if  all  beams  come  ^i  of  an  inch  too 
long.  Where  beams  are  to  be  built  into  the  wall,  order  them  in  full 
lengths  making  no  allowance  for  clearance.  Order  small  plates  in  mul- 
tiple lengths.  Irregular  plates  on  which  there  will  be  considerable 
waste  should  be  ordered  cut  to  templet.  Mills  will  not  make  reentrant 
cuts  in  plates.  Allow  %  of  an  inch  for  each  milling  for  members  that 
have  to  be  faced.  Order  web  plates  for  girders  *4  to  J/£  inch  narrower 
than  the  distance  back  to  back  of  angles.  Order  as  nearly  as  possible 
every  thing  cut  to  required  length,  except  where  there  is  liable  to  be 
changes  made,  in  which  case  order  long  lengths. 

It  is  often  possible  to  reduce  the  cost  of  mill  details  by  having  the 
mills  do  only  part  of  the  work,  the  rest  being  done  in  the  field,  or  by 
sending  out  from  the  shop  to  be  riveted  on  in  the  field  connection  angles 
and  other  small  details  that  would  cause  the  work  to  take  a  very  much 
higher  price.  Standard  connections  should  be  used  wherever  possible, 
and  special  work  should  be  avoided. 

The  classification  of  iron  and  steel  bars  is  given  in  Table  XXVII. 
The  full  extra  charges  for  sizes  other  than  those  taking  the  base  rate 
are  seldom  enforced ;  one-half  card  extras  being  very  common. 


352 


ESTIMATE  OF  WEIGHT  AND  COST 


TABLE  XXVII. 
Iron  Classification. 

Adopted  Dec  3,  1895,  by  National  Bar  Iron  Association. 
Adopted  March  16, 1899,  by  Eastern  Bar  Iron  Manufacturers'  Association. 


to  3l/2 


Hto  A 
Kto  A 


Rounds  and  Squares. 

Extra. 
.-  -  2A 

1 

Oval   Iron. 

Extra. 


Extra. 
Base  sizes  no  extra 


i* 

A 

ic. 

A 


Extra. 


Half  Oval  and  Half  Round. 

Extra. 
-- 4i 


Extra. 


::::::::::::::::::::::::::  $ 

Half  ovals  less  than  X  their  width  hi  thickness,  extra  price. 

Flats. 

Extra. 


it  to 

}4  to 

#to 

#  to 

ft  to 

Xto 

Xto  j 
to  i 
to  i 

^  to  i 

Y*  to  4 

l/2  to  4 

^  to  4 
to  4 
to  4 


Ax 

** 

X 


/z 

ft 


Xto 
X  to 
^to 
Xto 
}i  to 
Xto 
^  to 
Xto 
#to  # 
^  to  i 

Xto   A 
Htoi 

x  lA  to  x# 
x  l#  to  2 
x  2ji  to  3 


lA 
1C. 

T9* 


.Base  no  extra. 
* 

::::::::::  t 


4*4  to 
4V  to 


4Xto 
4Xto 
6Xto 
7  to  8 
6X  to  8 
6^to  8 
6X  to  8 
8X  to  10 
8X  to  10 
8X  to  10 
8X  to  10 


T5o' 


i#  to  2 

a^to  3 
Xto^  A 
Xto     A 
f^  to   i>^ 

l>^  to   2 

a^to  3 
^to    A 


irVto    i, 
I#  to  2 


Extra. 

II 

...  ic. 


Flats  A  thick  Ac.  per  Ib  higher  than  X  to  A  thick. 
Bevel  edge  Shaft  Iron  A.C.  higher  than  same  size  of  Flats. 
All  round  edge  iron  Ac.  per  Ib  extra. 
Horse  Shoe  Iron  all  sizes  ic.  extra. 


Light  Bands. 

Extra. 

^            xNos.  10,  Hand  12-  ......  iT6ir 

^8            x  No.  9  to  A  -------  .......  'T5* 

A  to  yz  x  Nos.  10,  II  and  12  .......  iA 

Ato^xNo.  9  to  A  .....  .  ......  _.  ,A 

T\  to  fs  x  Nos.  10,  II  and  12  ____  ...  iA 

to  f^  x  No.  9  to  A  _____  ........  --  Ic- 

to  X  *  Nos.  10,  II  and  12  _______  A 

to  MX  No.  9  to  A  ------  ........  A 

to  %  x  Nos.  10,  II  and  12  .......  A 

to  %  x  No.  9  to  A  ..............  A 


Extra. 

x  Nos.  10,  II  and  12    ^ 

to  iisff  K  No.  9  to  T3T ft 

T.%  to  4      xT^os.  10,  II  and  12 A 

1X104     x  No.  9  to  A _.    'ft 

414  to6      x  Nos.  10,  II  and  12 ft 

4^  to  6      x  Nos.  9  to  r\ T5g 

6X  to  6X  x  Nos.  10,  II -and  12 ft 

6X  to  6%  x  No.  9  to  A -    -A 

7      to  8      x  Nos.  10,  ii  and  12 ic. 

7      to8      x  No.  9  to  A ft, 


Bevel  Edge  Box  Iron  same  as  Light  Bands  of  same  sizes. 

Beaded  Band  Iron  iX  inch  to  2  inch  A  extra. 

Sand  Band  Iron  Ac.  above  same  sizes  of  Light  Bands. 


SHOP  COST  353 

Shop  Cost. — The  shop  cost  of  the  various  classes  of  work  is  a 
variable  quantity,  depending  upon  the  equipment  and  capacity  of  the 
shop,  the  number  of  pieces  made  alike,  the  familiarity  of  the  shop  men 
with  the  particular  class  of  work,  and  with  the  cost  of  labor.  The  costs 
given  below  are  the  average  costs  for  a  shop  with  a  capacity  of  about 
1000  tons  per  month  that  has  made  a  specialty  of  mill  building  work. 
The  costs  given  are  based  on  a  charge  of  40  cents  per  hour  for  the 
number  of  hours  actually  consumed  in  getting  out  the  contract.  This 
charge  is  assumed  to  cover  the  cost  of  management,  cost  of  operation 
and  maintenance,  as  well  as  the  cost  of  labor.  The  cost  of  management 
in  a  small  shop  is  very  small,  but  in  a  large  concern  it  may  amount  to 
as  much  as  35  to  40  per  cent  of  all  the  other  charges  combined.  For 
this  reason  small  structural  shops  can  often  fabricate  light  structural 
steel  for  a  less  cost  than  the  large  shops.  The  prices  given  are  about 
an  average  of  those  used  by  the  agents  of  the  company  above,  and  have 
been  checked  against  actual  costs  for  the  greater  part. 

Columns. — In  lots  of  at  least  six,  the  shop  cost  of  columns  is  about 
as  follows:  Columns  made  of  two  channels  and  two  plates,  or  two 
channels  laced  cost  about  0.80  to  0.70  cents  per  lb.,  for  columns  weigh- 
ing from  600  to  looo  Ibs.  each;  columns  made  of  4-angles  laced  cost 
from  0.80  to  i.io  cents  per  lb. ;  columns  made  of  two  channels  and 
one  I  beam,  or  three  channels  cost  from  0.65  to  0.90  cents  per  lb. ; 
columns  made  of  single  I  beams,  or  single  angles  cost  about  o .  50  cents 
per  lb. ;  and  Z-bar  columns  cost  from  0.70  to  0.90  cents  per  lb. 

Plain  cast  columns  cost  from  1.50  to  0.75  cents  per  lb.,  for  col- 
umns weighing  from  500  to  2500  Ibs.,  in  lots  of  at  least  six. 

Roof  Trusses. — In  lots  of  at  least  six,  the  shop  cost  of  ordinary 
riveted  roof  trusses  in  which  the  ends  of  the  members  are  cut  off  at 
right  angles  is  about  as  follows :  Trusses  weighing  1000  Ibs.  each,  1.15 
to  1.25  cents  per  lb. ;  trusses  weighing  1500  Ibs.  each,  0.90  to  i.oo 
cents  per  lb. ;  trusses  weighing  2500  Ibs.  each,  0.75  to  0.85  cents  per 
lb. ;  and  trusses  weighing  3500  to  7500  Ibs.  0.60  to  0.75  cents  per  lb. 
Pin  connected  truss.es  cost  from  o.io  to  0.20  cents  per  lb.  more  than 
riveted  trusses. 


354  ESTIMATE  OF  WEIGHT  AND  COST 

Have  Struts. — Ordinary  eave  struts  made  of  4-angles  laced,  whose 
length  does  not  exceed  20  to  30  feet,  cost  for  shop  work  from  0.80  to 
i.oo  cents  per  Ib. 

Plate  Girders. — The  shop  work  on  plate  girders  for  crane  girders 
and  floors  will  cost  from  0.60  to  1.25  cents  per  Ib.,  depending  upon  the 
weight,  details  and  number  made  at  one  time. 

Bye-Bars. — The  shop  cost  of  eye-bars  varies  with  the  size  and 
length  of  the  bars  and  the  number  made  alike.  The  following  costs 
are  a  fair  average:  Average  shop  cost  of  bars  3  inches  and  less  in 
width  and  ft  inches  and  less  in  thickness,  is  from  1 . 20  to  1 . 85  cents 
per  Ib.,  depending  on  length  and  size.  A  good  order  of  bars  running 
from  2^"  x  24"  to  3"  x  ft",  and  from  16  to  30  ft.  long,  with  few 
variations  in  size,  will  cost  about  1.20  cents  per  Ib.  Large  bars  in 
long  lengths  ordered  in  large  quantities  can  be  fabricated  at  from 
0.55  to  0.75  cents  per  Ib. 

To  get  the  total  cost  of  eye-bars  the  cost  of  bar  steel  must  be  added 
to  the  shop  cost. 

Cost  of  Drafting. — The  cost  per  ton  for  making  details  of  mill 
buildings  varies  with  the  character  of  the  work  and  the  tonnage  that  is 
to  be  fabricated  from  one  detail,  so  that  costs  per  ton  may  mean  very 
little.  The  following  will  give  an  idea  of  the  range  of  costs.  Details 
for  headworks  for  mines  cost  from  $4.00  to  $6.00  per  ton;  details 
for  church  and  court  house  roofs  having  hips  and  valleys  cost  from 
$6.00  to  $8.00  per  ton;  details  for  ordinary  mill  buildings  cost  from 
$2.00  to  $4.00  per  ton.  The  details  for  all  work  fabricated  by  the 
Gillette-Herzog  Mfg.  Co.,  with  the  exception  of  plain  beams  and  com- 
plicated tank  work,  were  made  in  1896  by  contract,  by  Mr.  H.  A.  Fitch, 
now  structural  engineer  for  the  Minneapolis  Steel  and  Machinery  Co., 
Minneapolis,  for  $2.06  per  ton.  This  price  netted  the  contractor  a  fair 
profit. 

Actual  Costs  of  Detailing. — The  details  of  the  building  for  which 
the  estimate  is  made  in  this  chapter  cost  $3 . 60  per  ton.  The  details  for 
the  Basin  &  Bay  State  Smelter,  Basin,  Montana,  containing  270  tons  of 
steel  cost  $2.00  per  ton. 


SHOP  COSTS  355 

Actual  Shop  Costs. — The  following  actual  shop  costs  will  give  an 
idea  of  the  range  of  costs :  The  shop  cost  of  the  transformer  building 
of  which  the  estimate  is  made  in  this  chapter  was  about  $20 .  oo  per  ton 
including  drafting;  the  Carbon  Tipple  building  at  Carbon,  Montana, 
weighing  86  tons,  cost  $18.60  per  ton.  The  shop  cost  of  the  structural 
work  of  the  East  Helena  transformer  building,  the  estimate  of  which 
is  given  in  the  next  to  the  last  column  in  Table  XXVT,  cost  $21.80  per 
ton  including  details.  The  shop  cost  of  the  Basin  &  Bay  State  smelter, 
weighing  270  tons,  was  $17.20  per  ton  including  details  which  cost  $2.00 
per  ton.  The  shop  cost  of  six  gallows  frames  made  by  the  Gillette-Her- 
zog  Mfg.  Co.,  varied  from  $21 .80  to  $41 .80  per  ton,  with  an  average  of 
$32.20  per  ton  including  details. 

Cost  of  Erection. — With  skilled  labor  at  $3 . 50  and  common  labor 
at  $2.00  per  day  of  9  hours,  small  buildings  like  those  given  in  Table 
XXVI  will  cost  about  $10.00  per  ton  for  the  erection  of  the  steel  frame- 
work, if  trusses  are  riveted  and  all  other  connections  are  bolted.  The 
cost  of  laying  corrugated  steel  is  about  $0.75  per  square  when  laid 
on  plank  sheathing,  $1.25  per  square  when  laid  directly  on  the  purlins, 
and  $2.00  per  square  when  laid  with  anti-condensation  roofing.  The 
erection  of  corrugated  steel  siding  costs  from  $o.  75  to  $i  .00  per  square. 
The  cost  of  erecting  heavy  machine  shops,  all  material  riveted  and  in- 
cluding the  cost  of  painting  but  not  the  cost  of  the  paint,  is  about  $8.50 
to  $9.00  per  ton.  Small  buildings  in  which  all  connections  are  bolted 
may  be  erected  for  from  $5.00  to  $6.00  per  ton.  The  cdst  of  erecting 
the  East  Helena  transformer  building  (next  to  the  last  building  in  Table 
XXVI)  was  $12.80  per  ton  including  the  erection  of  the  corrugated 
steel  and  transportation  of  the  men.  The  cost  of  erecting  the  Carbon 
Tipple  was  $8.80  per  ton  including  corrugated  steel.  The  cost  of 
erection  of  the  Basin  &  Bay  State  Smelter  was  $8.20  per  ton  including 
the  hoppers  and  corrugated  steel.  The  cost  of  erecting  6  gallows  frames 
in  Montana  varied  from  $11.20  to  $15.20  per  ton,  with  an  average  of 
813.00  per  ton,  all  connections  being  riveted. 

COST  OF  MISCELLANEOUS  MATERIAL.— In  making  an 
estimate  for  a  mill  building  the  engineer  needs  to  be  familiar  with  the 


356  ESTIMATE;  OF  WEIGHT  AND  COST 

costs  of  building  hardware,  lumber,  etc.  Prices  of  building  hardware 
are  usually  quoted  at  a  certain  discount  from  standard  lists.  These 
standard  lists  and  the  discounts  can  be  obtained  from  the 
dealers,  or  the  method  described  in  the  following  paragraph  may  be 
used. 

The  following  method  of  obtaining  costs  of  building  hardware 
and  other  miscellaneous  materials,  has  been  found  very  satisfactory: 
Obtain  standard  lists  from  the  dealers,  or  a  very  complete  one  entitled 
"The  Iron  Age  Standard  Hardware  Lists"  may  be  obtained  from  the 
David  Williams  Co.,  New  York,  for  $1.00,  postpaid.  To  find  the  cur- 
rent discount,  consult  the  current  number  of  the  Iron  Age,  or  a  simi- 
lar publication — the  Iron  Age  is  published  by  the  David  Williams  Co., 
New  York,  at  $5.00  per  year,  or  10  cents  per  single  copy,  and  gives 
each  week  the  current  hardware  prices  and  discounts.  By  applying 
the  discount  to  the  prices  given  in  the  standard  lists  the  current  price 
of  the  material  can  be  obtained.  The  standard  lists  of  machine  bolts, 
carriage  bolts,  nails,  and  turnbuckles  are  given  for  convenience  in  es- 
timating and  to  illustrate  what  is  meant  by  lists. 

To  illustrate  the  method  just  described  the  current  prices  (1903) 
will  be  obtained  for  a  few  items: 

2-in.  Barbed  Roofing  Nails. — The  base  price  of  nails  is  $2.65  per 
keg  of  100  Ibs.,  and  from  standard  nail  list  (Table  XXVIII)  we  see 
that  2-in.  barbed  roofing  nails  take  $0.35  per  100  Ibs.  advance  over  the 
base  price  making  the  price  $3.00  per  100  Ibs. 

Carriage  Bolts. — 2^/2"  x  j£"  carriage  bolts  are  listed  (Table 
XXVIII)  at  $3.00  per  100,  from  which  a  discount  of  60  and  10% 
is  allowed.  A  discount  of  60  and  10%  is  equivalent  to  a  discount 
of  64%,  making  the  price  of  the  bolts  $1.08  per  100. 

Machine  Bolts.— 4"  x  y2"  machine  bolts  are  listed  (Table  XXIX) 
at  $4.90  per  100,  from  which  a  discount  of  65  and  $%  is  allowed.  A 
discount  of  65  and  5%  is  equivalent  to  a  discount  of  66^4%,  making 
the  price  of  the  bolts  $i  .36  per  100.  The  weight  of  machine  bolts  and 
nuts  is  given,  from  which  the  price  per  Ib.  can  be  obtained  for  any  size 
of  bolt. 


STANDARD  HARDWARE  LISTS 


357 


The  following  approximate  prices  of  materials  will  assist  in  mak- 
ing preliminary  estimates:  rivets,  $2.25  to  $3.00  per  100  Ibs. ;  boat 
spikes,  $2.25  to  $3.00  per  100  Ibs.;  washers,  cut,  $6.00  per  100  Ibs.; 
washers,  cast,  $i . 50  to  $2.00  per  100  Ibs. ;  sash  weights,  $i  .00  to  $1 . 50 
per  loo  Ibs. ;  pins  $3.50  to  $4.0x3  per  100  Ibs. ;  pin  nuts,  $4.00  per  100 
Ibs. ;  wire  poultry  netting,  $0.50  per  square ;  asbestos  felt,  32  Ibs.  to  the 
square,  $2.75  to  $3.00  per  100  Ibs. ;  turnbuckles,  50%  discount.  Other 
prices  and  costs  will  be  found  in  the  descriptions  of  the  various  articles 
on  the  preceding  pages. 

TABLE  XXVIII. 


LIST  ADOPTED  DECEMBER  1,  1896. 
STEEL   WIRE    NAILS. 


Common, 

Fence 

and 

Brads. 


30d  to  60d Base. 

lOd  to  16d $0.05  extra  per  keg. 

8dand9d 10      "  • 

6dand7d 20      «• 

4dand5d 30      * 

3d 45      * 

2d 70      • 


Barbed  Common  and  Barbed  Car  Nails,  I5c.  advance  over 

Fine  Nail« 

(Extra  per  keg) 


Casing  and  Smooth  Box  JfaUi— (Extra  per  keg). 
304*>d20dl2Al«dlOd8Jt9dei7d5d      4d      3d      W 


tO. 15        .IS          .15          .15 


.as     .so    .so    .70  1.09 


.SOd  1Z  A  1M  lOd  8  <k  9d  «  *  Td  5d    4d    3d    Id 


(Extra  per  keg).».8S      . 
Barrel 1H  in. 


.35         .45     .65    .65    .85  1  15 
Hi        1H          1  X  k 


(Kxia  per  keg).    1030        .40       .SO       .90       .70       .85       1.00 

Clinch SOd  12*16d  lOd  84M  «A7d  4ASd  3d    M 

(Extra  per  keg). » 35      !»       !»      Is        ]» 

Barbed  Roofing.    Zin.         1J£       1>4       ifc" 
(Extra  per  keg)     «0.35         li        !«        i» 

Wire  spikes,  all  size* 


Common  Carriage 

Bolts.  JS.1^.— 

Length 

9  16 

in  Inches. 

14 

516 

S-8 

7  IS 

1-2 

458 

34 

1J£ 

$1.00 

$1.20 

$1.60 

$2.20 

Hi 

1.04 

1.25 

1.68 

2.29 

t 

1.08 

1.30 

1.76 

2.38 

1.12 

1  35 

1.84 

247 

*£l£ 

1.16 

1.40 

1.93 

256 

$300 

$5.20 

$7.20 

%% 

1.20 

1.45 

200 

2.65 

311 

5.37 

74* 

3 

124 

150 

2.08 

2.74 

3.22 

554 

7.66 

1  28 

1.55 

2.16 

283 

333 

5.71 

7.89 

1  S2 

160 

2.24 

292 

3.44 

5.88 

8.12 

1.36 

1.65 

2.32 

3.01 

855 

605 

8.35 

1.40 

1.70 

240 

3  10 

3.66 

6.22 

8.58 

£U 

1.44 

1.75 

2.48 

3.19 

3.77 

8.81 

412 

1  48 

1.80 

2.56 

3.28 

3.88 

&56 

904 

vZ 

1  52. 

1.85 

2.64 

337 

3.99 

6.73 

927 

• 

1.56 

1.90 

2.73 

3.46 

4.10 

6.90 

9.50 

S1^ 

1.64 

2.00 

2.8S 

3.64 

4.32 

7.24 

9.96 

« 

1.72 

2.10 

3.04 

8.83 

4.54 

758 

10.43 

Stf 

IHO 

2.20 

3.20 

4.00 

4.76 

7.92 

10.8S 

7 

1.88 

230 

336 

4.18 

4.98 

8.26 

1134 

73^ 

1  96 

2.40 

3.52 

4.36 

520 

8.60 

11.80 

8 

2.04 

250 

36* 

4.54 

5.43 

8.94 

12.26 

M/ 

2.12 

260 

3.84 

4.72 

5.64 

928 

12.72 

9 

2.20 

270 

400 

4.90 

5.86 

962 

13  18 

9-; 

2.28 

2.80 

416 

6.08 

6.08 

996 

13.64 

10 

2.36 

2.90 

4.32 

5.26 

630 

10.30 

1410 

11 

2.52 

3.10 

464 

5.62 

6.74 

1098 

1503 

12 

2.68 

3.30 

4.96 

5.98 

7.18 

11.66 

15.94 

n 

2.84 

8.50 

5.28 

684 

7.62 

12.34 

16.86 

14 

3.00 

3.70 

5.60 

6-50 

8.06 

13.02 

17.78 

IS 

8  16 

3.90 

5.92 

7.06 

8.50 

18.70 

16 

3.32 

4.10 

6.24 

7.42 

894 

14.38 

19.62 

17 

348 

4.30 

6.56 

7.78 

9.3S 

1506 

2054 

18 

3.64 

450 

6.88 

814 

9.82 

15.74 

21.46 

8 

3.80 
396 

470 
4.90 

7.<0 
7.52 

8.50 
8.86 

1026 
10.70 

16.42 
17.10 

2234 
23.30 

LENGTH   AND   APPROXIMATE   GAUGE   OF  COMMON 
WIRE   NAILS. 


No.  9 


ft    *& 


ZOd          30d          40d          SOd         «0d; 


Turnbuckles. 


C 


1-75 

2.  CO 
2-25 
2.^5 

J.  10 

5-50 
4.00 

4- so 


a 


5.50 

6.00 
6.50 
7-50 
8.00 
9.00 

10. OO 

15.00 

20.00 


SPIKES,  NAILS  AND  TACKS. 


WIRE  NAILS. 


Sizes.    Length. 


m 

Ml 

toa 


.0641 

.0641 
.0720 

.«nt 


STEEL  WIRE  SPIKES. 


358 


ESTIMATE;  OF  WEIGHT  AND  COST 
TABLE  XXIX. 


MANUFACTURERS1  STANDARD  LIST  Of 

MACHINE    BOLTS    WITH     SQUARE    HEADS   AND 

SQUARE  NUTS.     FINISHED  POINTS. 

PRICE  PER  HUNDRED. 


L.ng1h 
Inch**. 

*   1* 

1  |A 

i 

A*I 

} 

i 

1 

~1T" 

OoOo 

Oottlo 

3.60 

Tao 

TTo 

10.50 

15.10 

2* 

1.78 

2.12 

2.563.00 

3.86 

5.58 

7.70 

11.20 

16.00 

1.86 

2.24 

2.723.20 

.12 

5.96 

8.20 

11.90 

16.90 

1.94 

2.36 

2.883.40 

.38 

6.34 

8.70 

12.60 

17.80 

n 

2.02 

3.48 

3.043.60 

.64 

6.72 

9.20 

13.30 

18.70 

4 

3.10 

2.003.2013.80 

.90 

7.10 

9.70 

14.00 

19.60 

41 

l.tt 

2.723.364.00 

.16 

7.48 

10.20 

14.70 

20.50 

f 

I.M 

2.843.524.20 

.42 

7.86 

10.70 

15.40 

21.40 

• 

2.34 

2.963.684.40 

.68 

8.24 

11.20 

16.10 

22.30 

6* 

2.42 

3.083.8414.60 

.94 

8.62 

11.70 

16.80 

23.20 

«1 

I.H 

3.20 

4.004.80 

.20 

9.00 

12.20 

17.50 

24.10 

7 

3.58 

I.M 

4.165.00 

.46 

9.38 

12.70 

18.20 

25.00 

'* 

2  80 

3.44 

4.325.20 

.72 

9.76 

13.20 

18.90 

25.90 

8 

l.«| 

i.r.i; 

4  485.40 

.98 

10.14 

13.70 

19.60 

26.80 

e 

2.90 

3.80 

4.  8015.80 

7.50 

10.90 

14.70 

21.00 

28.60 

10 

I.M 

4.04 

5.126.20 

8.02 

11.66 

15.70 

22.40 

30.40 

11 

J   L"J 

I.M 

5.44'6.60 

8.54 

12.42 

16.70 

23.80 

32.20 

la 

3.3S 

4.52 

5.76 

7.00 

9.06 

13.18 

17.70 

25.20 

34.00 

18 

6.08 

7.40 

9.58 

13.94 

18.70 

26.60 

35.80 

14 
15 

.... 

6.40 
6.72 

7.80 
8.20 

10.10 
10.62 

14.70 
15.46 

19.70 
20.70 

28.00 
29.40 

37.60 
39.40 

18 

7.04 

8.60 

11.14 

16.22 

21.70 

30.80 

41.20 

17 

11.66 

16.98 

22.70 

32.20 

43.00 

18 

12  18 

17.74 

33.70 

33.60 

44.80 

19 

L2i70 

18.50 

24.70 

35.00 

46.60 

20 

13.22 

19.26 

,25.70 

36.40 

48.40 

21 

26.70 

37.80 

50.20 

23 

27.70 

39.20 

52.00 

28 

28.70 

40.60 

53.80 

24 

29.70 

42.00 

55.60 

25 

30.70 

43.40 

57.40 

26 

31.70 

44.80 

59.20 

27 

1°  70 

46.20 

RI  on 

28 

1?  70 

47.60  62.80 

29 

34.70 

49  00  64.60 

30 

35.70 

50.  40  166.  40 

The  following:  extras  are  to  be  understood  as  a  part  of  the 

Bolts  with  Hexagon  Heads  or  Hexagon  Nuts,  10  per  cent  extra. 

If  both  Hexagon  Heads  and  Hexagon  Nuts,  20  per  cent  extra. 

Joint  Bolts  with  Oblong  Nuts,  Bolts  with  Tee  Heads,  Askew 
Beads,  and  Eccentric  Heads,  10  per  cent  extra. 

Special  Bolts  with  irregular  Threads  and  unusual  dimensions 
of  Heads  or  Nuts  will  be  charged  extra  at  the  discretion  of  the 


AVERAGE  WEIGHT  OF  SQUARE  HEAD 
MACHINE  BOLTS  PER  1OO. 


Length. 

DIAMETER. 

K 

A 

X 

/. 

u 

X 

X 

X 

-|  j  ;  j  j  i  ;s*lsllsiliisiiiiiisi5si 

P 

P 

z 

6* 

£ 

h 

r 

10 
11 

12 

18 
16 
SO 

4.0 
4.4 

!:I 

Is 

7.5 

H 

96 

0.8 
8^4 

1:1 

10.0 

iii 

154 

10.6 
11.8 
12.0 
126 
13  3 
14.0 

III 
17.4 

21-4 

15.0 
16.1 
17.2 
18.2 

11 
25.8 
27.8 
29.1 
81.2 

23.9 

25.1 
26.3 
27.7 

II 
87.5 
40.2 
43.0 
45.7 

40.5 
42.7 
44.8 
47.0 

S3 
53.5 
57.9 
62.8 

75^4 

70.0 
73.1 
76.2 
79.8 
824 

8:? 
loti 

107.6 
118.7 
120.0 
1262 
132.5 
138.7 
1450 
151.2 
163.7 
176.2 
188.7 
201.0 
213.4 
2259 

31 

263.2 
275.6 
288.1 
300.6 

Si? 

128.9 
137.4 
145.8 
159.2 
167.7 
176.1 
184.6 
183.0 
201.4 
809  9 
218.3 
240.2 
257.1 
273.9 
290.0 
807.7 
3*4.5 
841.4 

sJ 

3920 
408  9 
425.8 

11.7 
12.4 
18.1 

17.6 
186 
19.7 
20.8 

24.1 
259 
27.7 
29.5 
83  1 
367 
40.4 
44.0 

85.1 
37.1 

53^0 
51.0 

61.2 
54.0 
58.7 
59.4 
64.8 
76.8' 
75.8 
81.8 
86.7 
922 
97.7 
103.1 

BS:? 

119.5 
125.0 

88.5 
183:5 

%? 

149.2 
157.6 
166.1 
174.« 
183.1 
191.5 
200.0 

::::: 

:::::: 

Per 

1.4 

2.8 

86 

4.0 

55 

8.5 

18.4 

16.9 

SS.O 

APPROXIMATE  WEIGHT  OF  NUTS  AND  BOLT 
HEADS.  IN  POUNDS. 


Diam.  of  Bolt  In  Inches, 
vVeight  of  Hexagon  Nut  I 
Wefgjht 6of  Siuaw 'iJut  [ 


Diam  of  Bolt  in  inches. 


PART  IV. 

MISCELLANEOUS  STRUCTURES, 

The  descriptions  of  the  different  structures  given  in  this  part  have 
been  abstracted  from  descriptions  published  in  the  Engineering  News, 
Engineering  Record,  etc.  Figs.  171  and  172  are  from  the  Railroad 
Gazette ;  and  Fig.  169  and  Figs.  172  to  181,  inclusive,  are  reproduced 
from  originals  kindly  loaned  by  the  Engineering  News. 

STEEL  DOME  FOR  THE  WEST  BADEN,  IND.,  HOTEL.* 

The  dome  of  the  new  hotel  at  West  Baden,  Ind.,  is  remarkable  for 
its  size.  This  dome  has  a  steel  framework  and  is  larger  than  any  other 
ever  built,  its  span  exceeding  by  about  15  feet  that  of  the  Horticultural 
Building  of  the  Chicago  Exposition  of  1893. 

The  dome  is  about  200  feet  in  outside  diameter  and  rises  about  50 
feet  above  the  bed  plates.  Its  frame  consists  of  24  steel  ribs,  all  con- 
nected at  the  center  or  crown  to  a  circular  plate  drum,  and  tied  together 
at  the  bottom  by  a  circular  plate  girder  tie.  Each  rib  foots  at  its  out- 
side end  on  a  built  up  steel  shoe,  resting  on  a  masonry  pier.  The  rib 
is  connected  to  the  shoe  by  a  steel  pin,  and  the  outside  plate  girder  toe 
is  attached  to  the  gusset  plate  at  this  point,  just  above  the  shoe.  The 
shoes  of  all  the  girders  are  constructed  as  expansion  bearings,  being 
provided  with  rollers  in  the  usual  manner. 

The  dome  is  therefore  virtually  an  aggregation  of  two-hinged 
arches  with  the  drum  at  the  center  forming  their  common  connection. 
Their  thrust  at  the  foot  goes  into  the  circular  tie-girder,  and  only  ver- 
tical loads  (and  wind  loads)  come  upon  the  shoes  and  the  bearing  piers. 
At  the  same  time  any  temperature  stresses  are  avoided,  since  the  ex- 
pansion rollers  under  the  shoes  permit  a  uniform  outward  motion  of 
the  lower  ends  of  all  the  ribs. 

The  outline  of  the  dome  and  part  of  the  dome  framing  are  shown 

•Engineering  News,  Sept,  4,  1902. 


36o 


MISCELLANEOUS  STRUCTURES 


DOME  FOR  WEST  BADEN  HOTEL  361 

in  Fig.  169.  The  rise  is  between  l/±  and  ^  of  the  span.  The  outline 
of  the  top  chord  approximates  an  elliptical  curve,  and  the  bottom  chord 
is  parallel  to  the  top  chord  throughout  its  length,  except  in  the  three  end 
panels  on  either  side;  the  depth  of  the  arch  being  10  ft.  back  to  back 
of  chord  angles.  The  web  members  are  arranged  as  a  single  system  of 
the  Pratt  type,  with  substruts  to  the  top  chord  as  purlin  supports.  In 
the  end  sections  the  arrangement  is  necessarily  modified,  the  sharper 
curvature  of  the  chords  being  allowed  for  by  more  frequent  strutting. 

The  maximum  stresses  in  the  different  members  of  the  arch  are 
given  on  the  right  half  of  the  rib  in  Fig.  169.  They  are  obtained  by 
properly  combining  the  dead  load  stresses  with  the  stresses  due  to  wind 
blowing  successively  in  opposite  directions  in  the  plane  of  the  rib  in 
question.  The  loads  used  in  the  calculation  were  a  dead  load  separate- 
ly estimated  for  each  panel  point,  a  variable  snow  load,  heaviest  at  the 
center  of  the  roof,  a  wind  load  of  30  Ibs,  per  sq.  ft.  on  a  normal  surface 
reduced  for  inclination  of  the  roof  to  the  vertical.  The  makeup  of  the 
members  is  given  on  the  left  half  of  the  rib  in  Fig.  169.  In  the  plan 
part  of  the  dome  the  method  of  bracing  the  ribs  is  fully  shown.  Suc- 
cessive pairs  of  ribs  are  connected  by  bays  of  bracing  in  both  upper 
and  lower  chords.  In  the  upper  chord  the  I  beam  purlins  are  made  use 
of  as  struts,  angle  struts  being  used  in  the  lower  chord.  The  bracing 
consists  throughout  of  crossed  adjustable  rods.  At  the  center,  these 
rods  are  carried  over  to  a  tangential  attachment  to  the  central  drum,  so 
as  to  give  more  rigidity  against  twisting  at  the  center. 

The  central  drum,  16  ft.  in  diameter  by  10  ft.  deep,  has  a  web  of 
y%  inch  plate,  with  stiffener  angles  to  which  the  ribs  are  attached.  At 
top  and  bottom  the  drum  carries  a  flange  plate  24  ins.  x  3-16  ins.  for 
lateral  stiffeners.  In  addition  it  is  cross  braced  internally  by  four 
diametrical  frames  intersecting  at  the  center.  The  outer  tie-girder, 
which  takes  the  thrust  of  the  arch  ribs,  is  a  simple  channel-shaped  plate 
girder,  24  ins.  deep,  as  shown  on  the  plan.  The  weight  of  the  dome 
complete,  including  framework  and  covering  was  475,000  Ibs.  This 
makes  the  dead  load  about  15  Ibs.  per  square  foot  of  horizontal  projec- 
tion of  roof  surface. 

Mr.  Harrison  Albright,  of  Charleston,  W.  Va.,  was  the  architect  of 
the  building  and  the  design  of  the  steel  dome  was  worked  out  by  Mr. 
Oliver  J.  Westcott,  while  in  charge  of  the  estimating  department  of 
the  Illinois  Steel  Company.  The  structural  steel  was  furnished  by  the 
Illinois  Steel  Co. 


THE  ST.  Louis  COLISEUM.* 

The  St.  Louis  Coliseum  Building  is  a  rectangular  brick  building 
1 86'  2"  x  322'  3".  The  steel  framework  is  made  entirely  independent  of 
the  masonry  walls  and  consists  of  three-hinged  arches  properly  braced. 
The  Coliseum  has  an  area  of  222  x  112  feet  clear  of  the  curb  wall. 
Ordinarily  there  are  seats  for  7,000  persons  on  the  main  floor  and  the 
galleries,  but  for  convention  purposes  with  seats  in  the  arena  the  num- 
ber can  be  increased  to  12,000  persons. 

The  steel  framework  consists  of  a  central  arched  section  adjoined  at 
each  end  by  a  half  dome  formed  by  six  radial  arched  trusses.  The  main 
arches  forming  the  central  section  have  a  span  178'  6"  c.  to  c.  of  shoe 
pins,  are  spaced  36'  8"  apart,  and  are  connected  by  lateral  bracing  in 
pairs.  The  pins  at  the  foot  of  the  arches  are  4  7-16"  diameter,  and  at 
the  crown  the  pin  is  2  5-16"  diameter.  The  rise  of  the  arches  is  80'  o", 
the  lower  chord  points  being  in  the  curve  of  a  true  ellipse. 

The  end  radial  trusses  correspond  essentially  to  the  semi-trusses  of 
the  main  arches  except  for  their  top  connection,  where  their  top  chords 
are  attached  to  a  semicircular  frame  supported  by  the  end  main  trusses 
and  designed  to  receive  thrust,  but  no  vertical  reaction,  as  shown  in 
Fig.  170. 

The  roof  covering  of  asphalt  composition  is  laid  on  i^-inch  boards, 
resting  on  2^  x  i6-inch  wood  joists,  3  feet  apart  and  ceiled  underneath. 
These,  in  turn,  are  carried  by  the  steel  purlins  of  the  structure,  which 
are  spaced  about  16  feet  apart.  The  gallery  floor  beams  are  carried  on 
stringers  of  8-inch  channels  spaced  3'  8"  center  to  center,  carried  by 
girders  running  between,  and  supported  by  the  arches.  The  rear  string- 
er is  a  plate  girder ;  the  front  one  is  a  latticed  girder,  the  gallery  beams 
running  through  the  latter  and  cantilevering  out  5'  4".  The  main  floor 
beams,  supporting  the  lower  tier  of  seats,  consist  of  9-inch  I  beams, 
spaced  3'  8"  center  to  center,  which  are  similarly  carried  on  girders,  and 
their  lower  ends  rest  on  a  brick  wall. 


*Engineering  News,  Aug.   10,   1899,  and  Engineering  Record,  1899. 


THE  ST.  Louis  COLISEUM 


363 


Sectional  Plan 
Rgure  I.    General  Plan  of  Trusses& Framing 


& 


--fe: 


***J 

£@/\ 


Ran  of  Half  Ring  Connecting 
Radial  Trusses  to  Main  Trusses 


Main  Arches 

Figure  2  -  Cross  Section  Showing  Construction  of  Main  Arches 

FIG.  170. 

The  loads,  in  accordance  with  which  the  trusses  were  figured,  are 
as  follows: 

CASE  I. 

Wooden  deck  and  gravel  of  roof 17.5  Ibs.  per  sq.  ft.,  vertically 

Steel    12.5    "      "     "     " 

Snow   and  wind    25  .o    "      "     "     " 


Total 
25 


55-0    " 


364  MISCELLANEOUS  STRUCTURES 

Add  for  floors,  viz.: 

Main  floors,  banks  and  galleries 105.0    "      "     "     " 

Attic  floors    60. p    "      "     "     " 

CASE  II. 

Wooden  deck  and  gravel  of  roof 17.5  Ibs.  per  sq.  ft.,  vertically 

Steel    12.5    "      "     "     " 

Snow 10. o    "      "     "     " 

Total   40.0    "      "     "     " 

Wind   pressure  over  entire   elevation   of 

wall  and  roof  of 30.0  Ibs.  per  sq.  ft.,  horizontally 

LOADS  ON  PURLINS. 

Wooden  deck  and  gravel  of  roof 17.5  Ibs.  per  sq.  ft.,  vertically 

Steel    3.5    "      "     "     " 

Snow  and  wind 25.0"      "     "     " 


Total 46.0    "      "     "     " 

LOADS  ON  FLOOR  BEAMS,  GIRDERS  AND  COLUMNS  OF  MAIN  FLOORS. 

Banks  and  galleries,  beams 140  Ibs.  per  sq.  ft. 

Banks  and  galleries,  girders 112    "      "     "     " 

Banks  and  galleries,  columns 105    "      "     "     " 

Attic  floors  beams,  columns  and  girders 60    "      "     "     " 

For  the  main  trusses,  in  addition  to  the  stresses  of  Case  II.,  there 
was  added  the  stress  due  to  the  wind  bracing  between  these  trusses. 

For  the  radial  trusses,  in  addition  to  loading  of  Case  II.,  there 
was  assumed  an  additional  load  of  50,000  pounds  supposed  to  act  up 
or  down  at  the  upper  point  of  truss ;  this  load  being  what  was  assumed 
probable  in  case 'there  was  slight  unequal  settlement  of  the  footings. 

For  the  half  ring  connecting  the  tops  of  the  radial  trusses  there 
was  another  case  assumed,  beside  Cases  I.  and  II. — viz.,  a  tHrust  of 
50,000  pounds  at  any.  point  of  the  half  ring ;  this  being  the  thrust  of  a 
radial  truss  under  its  full  live  and  wind  load. 

All  the  material  used  was  of  medium  steel,  excepting  the  rivets, 
which  were  made  of  soft  steel.  Both  material  and  workmanship  con- 
form to  manufacturer's  standard  specifications. 


THE  ST.  Louis  COUSEUM  365 

UNIT  STRAINS. 

Tension 16,000  Ibs.  per  sq.  in, 

Compression,  for  lengths  of  90  radii  or  under.  . . .  12,000    "      u     "     " 

Compression,  for  lengths  of  over  90  radii 17,100 — 57  I  ~-  r 

Combined  stress  due  to  tension  or  compression 

and  transverse  loading 16,000    "      "     "     " 

Shear  on  web  plates  7,500    "      "     "     " 

Shear  on  pins  1 1,000    "      "     "     " 

Shear  on  rivets 10,000    "      "     "     " 

Bearing  on  pins   22,000    "      "     "     " 

Bearing  on  rivets 20,000    "      "     "     " 

Bending,  extreme  fibre  of  pins 25,000    "      "     "     " 

Bending,  extreme  fibre  of  beams 16,000    "      "     "     " 

Lateral  connections  have  25  per  cent  greater  unit  strains  than  the 
above. 

In  Case  II  of  trusses,  the  above  unit  strains  were  increased  one- 
third.  The  main  and  radial  arch  trusses  are  built  a*  shown  in  Fig. 
170,  except  that  above  the  haunches  the  ribs  of  the  radial  arches  are 
T-shaped  instead  of  I-shaped,  i.  e.,  they  have  no  inside  flanges.  The 
purlins  are  triangular  trusses  4^  feet  deep,  made  of  angles.  The  brac- 
ing between  main  arch  trusses  terminates  at  the  bottom  with  heavy 
portal  struts  of  triangular  box  section.  The  lateral  rods  are  not  car- 
ried" to  the  ground  on  account  of  the  obstruction  they  would  make.  The 
radial  trusses  are  coupled  together  in  pairs  with  lateral  rods  down  to 
the  ceiling  line.  The  thrust  due  to  wind  is  transmitted  from  them  into 
the  line  of  girders  around  the  structure  at  this  point,  and  into  the  ad- 
joining floor  systems.  The  compression  ribs  of  the  main  and  radial 
arches  are  stayed  laterally  by  angle  iron  ties,  connecting  to  the  first 
panel-point  in  the  bottom  chord  of  the  purlins.  In  the  planes  of  the 
first  diagonal  braces  of  the  trusses  above  the  haunches,  diagonal  rods 
connect  the  bottom  ribs  of  the  trusses  to  the  upper  ribs  of  the  next 
trusses.  No  struts  were  used  between  the  bottom  chords,  as  they  would 
have  been  directly  in  the  line  of  vision  from  the  rear  gallery  seats  to  the 
farther  end  of  the  arena.  The  front  and  rear  girders  supporting  the 
gallery  and  main  floor  beams  are  tied  together  with  a  triangular  system 
of  angle  iron  bracing. 

To  provide  for  expansion,  the  radial  purlins  and  all  the  girders  be- 
tween the  arches  have  slotted  hole  connections  in  every  alternate  bay. 
The  diagonal  rods  between  the  two  lines  of  ridge  purlins  were  tightly 


366 


MISCELLANEOUS  STRUCTURES 


adjusted  on  a  hot  day.  To  prevent  secondary  strains  in  the  half  ring 
to  which  the  radial  trusses  are  connected  at  their  tops,  there  is  i-i6-inch 
clearance  in  all  the  pin  holes.  There  is  also  clearance  between  the  pin 
plates,  so  that  the  trusses  and  the  ring  can  slide  a  little  sideways  on 
their  pins.  The  lines  of  the  arch  trusses  were  laid  out  full  size  and  the 
principal  points  checked  by  independent  measurements  in  the  template 
shop,  and  the  work  was  accurately  assembled.  In  order  to  avoid  the 
handling  of  large,  heavy  pieces  before  the  drill  press,  the  foot  of  the 
arch,  through  which  the  pin  hole  was  bored,  was  made  separately  and 
afterward  riveted  on. 

The  total  weight  of  the  iron  in  the  entire  structure  was  1,905,000 
pounds,  as  follows:  Main  arches,  64,000  pounds,  each;  radial  arches 
21,000  pounds,  each;  purlins  between  main  trusses  1,450  pQunds,  each; 
main  floor  stringers  810  pounds,  each;  balcony  floor  stringers,  280 
pounds,  each;  cast  shoes  3,000  pounds,  each.  There  were  4,188  days 
labor  spent  on  the  work  in  the  shop  and  3,550  days  labor  during  erec- 
tion, the  average  number  of  men  in  the  erecting  force  being  about  50. 
The  stress  diagrams  and  detail  plans  of  the  steel  frame  were  made  un- 
der the  supervision  of  Mr.  Stern,  in  the  office  of  the  Koken  Iron  Works, 
who  were  contractors  for  the  ironwork,  and  were  submitted  for  approv- 
al to  the  consulting  engineer,  Mr.  Julius  Baier,  Assoc.  M.  Am.  Soc. 
C.  E.  Mr.  C.  K.  Ramsey  was  the  architect  of  the  Coliseum,  and  Mr. 
L.  H.  Sullivan  was  the  consulting  architect.  Mr.  A.  H.  Zeller  was 
consulting  engineer  for  the  Board  of  Public  Improvements ;  Mr.  J.  D. 
McKee,  C.  E.,  was  shop  inspector,  and  the  Hill-O'Meara  Construction 
Company  was  the  general  contractor. 


THE  LOCOMOTIVE  SHOPS  OF  THE  ATCHISON,  TOPEKA  AND  SANTA  FE 
R.  R.,  TOPEKA,  KAS.* 

This  building  is  intended  for  all  the  locomotive  work,  including 
boilers  and  tenders.  It  is  of  particular  note  for  its  great  size  and  the 
peculiar  features  of  its  design.  In  general  plan  it  is  852  ft.  long  and  153 
ft.  10  ins.  wide,  the  width  being  divided  into  a  center  span  of  74  ft.  3 
ins.  and  two  side  spans  of  39  ft.  9  ins.  It  is  of  self-supporting  steel 
frame  construction,  with  concrete  foundations  and  floor,  13-in.  brick 
walls,  and  Ludowici  tile  roof.  There  is  no  sheathing  under  the  tiles, 
which  thus  constitute  the  sole  covering.  The  tiles  are  laid  on  2  x  2-in. 
timber  strips  to  which  every  fourth  tile  is  fastened  by  copper  wire. 

The  most  striking  feature  of  the  design  is  that  the  saw  tooth  or 
weaving  shed  type  of  roof  is  adopted  for  the  side  spans,  the  glazed 
vertical  sides  of  the  ridges  facing  northward.  This  feature  was  intro- 
duced with  the  view  of  making  the  shop  as  light  as  possible.  The  ar- 
rangement could  not  well  be  used  where  heavy  snows  are  frequently 
experienced,  as  the  snow  would  pack  between  the  ridges,  but  there  are 
comparatively  few  heavy  snow  storms  in  the  vicinity  of  Topeka.  In 
addition  to  this  arrangement,  the  greater  proportion  of  the  area  of  the 
side  walls  is  composed  of  windows,  while  the  exposed  parts  of  the 
sides  of  the  central  span  (between  the  ridges  of  the  side  spans)  are 
also  glazed.  There  are  also  several  windows  in  the  end  walls.  The 
roof  of  the  central  span  has  on  each  side  of  the  ridge  a  skylight  12  ft. 
wide,  extending  the  full  length  of  the  building.  These  skylights  are 
fitted  with  translucent  fabric  instead  of  glass.  By  these  various  means 
an  exceptionally  good  lighting  effect  and  diffusion  of  light  are  obtained 
and  the  shop  is  in  fact  remarkably  light  even  on  a  gloomy  day.  There 
is  no  monitor  roof,  but  ventilation  is  provided  for  by  Star  ventilators 
25  ft.  apart  along  the  ridge  of  the  main  roof. 

The  columns  are  built  up  of  pairs  of  15-in.  channels,  and  independ- 
ent columns  of  similar  construction  carry  the  double-web  box  girder 
runways  for  the  electric  traveling  cranes  which  run  the  entire  length 
of  the  central  span.  Fig.  173  shows  the  elevations,  sections  and  plans 

•Engineering  News,  Jan.  3,  1903:  and  Railway  Gazette,  Nov.  7,  1902. 


368 


MISCELLANEOUS  STRUCTURES 


FIG.  171.    LOCOMOTIVE  SHOP. 


FIG.  172.    CROSS-SECTION  LOCOMOTIVE  SHOP. 

of  the  steel  structural  framework,  and  Fig.  174  is  a  partial  elevation  on 
the  east  side.  Fig.  175  shows  the  design  of  the  central  roof  trusses  and 
the  lattice  girders  which  form  longitudinal  bracing  between  the  trusses. 
This  longitudinal  bracing  is  not  continuous  but  is  fitted  only  between 


LOCOMOTIVE  SHOPS,  A.  T.  &  S.  F.  R.  R. 


369 


alternate  pairs  of  trusses.  End  trusses  are  built  into  the  walls,  as 
these  walls  are  pierced  by  numerous  windows  and  doors  and  are  not 
relied  upon  in  any  way  to  support  the  roof.  Portal  bracing  is  fitted 
between  the  side  or  wall  columns  at  intervals.  No  metal  less  than  jHj-in. 
thick  is  used  in  the  structural  work. 


ElevaTion  O-M. 

Cross  Section  of  Boiler  Shop. 

FIG.  173.    PART  ELEVATIONS  AND  PLANS  OF  STEEL  STRUCTURAL  WORK 

OF  NEW  LOCOMOTIVE  SHOPS. 


The  roof  trusses  are  proportioned  for  a  load  of  15  Ibs.  per  sq.  ft. 
for  the  weight  of  the  roofing,  10  Ibs.  per  sq.  ft.  for  snow,  and  25  Ibs. 
per  sq.  ft.  for  wind  pressure,  or  50  Ibs.  per  sq.  ft.  in  all.  The  members 


frirn'ffT^^ 


rfrjrrm 


FIG.  174.    HALF  EAST  ELEVATION  OF  NEW  LOCOMOTIVE  SHOP. 
(SHOWING  RIVETING  TOWER  AND  WEAVING  SHED  ROOF.) 


37° 


MISCELLANEOUS  STRUCTURES. 


were  calculated  on  a  basis  of  16,000  Ibs.  per  sq.  in.  for  tension  and 
14,000  Ibs.  per  sq.  in.  for  compression.  Provision  for  expansion  and 
contraction  is  made  at  intervals  of  100  ft.  The  structural  work  for  this 
shop  was  built  at  the  Toledo  Works  of  the  American  Bridge  Co.  The 
steel  is  painted  a  light  grey,  and  the  brick  is  whitewashed,  a  pneumatic 
machine  being  used  for  the  latter  work. 

e'l- 


Half          Side  Elevation. 


* - 25'0'C.toC.of  Trusses 

Half         Transverse 

FIG.  175- 


Section. 


The  arrangements  for  lighting  the  shop  by  day  have  already  been 
referred  to.  For  night  work  there  will  be  arc  lights  for  general  light- 
ing and  incandescent  lamps  convenient  to  the  tools,  etc.  The  building 
is  heated  by  the  Sturtevant  hot  blast  system.  On  each  side  are  two 
fan  rooms,  each  containing  a  steam-driven  blower  fan  and  a  heating 


LOCOMOTIVE  SHOPS,  A.  T.  &  S.  F.  R.  R.  371 

chamber  filled  with  coils  of  pipe  through  which  passes  the  exhaust 
steam.  The  hot  air  is  delivered  into  two  longitudinal  underground  con- 
duits parallel  with  the  lines  of  columns,  with  a  duct  leading  to  the  sur- 
face at  each  column.  Each  duct  is  fitted  with  a  vertical  sheet  iron  pipe 
7  ft.  high,  with  a  flaring  head  to  deliver  the  air  horizontally.  The  plant 
is  guaranteed  to  maintain  a  temperature  of  70°  F.  throughout  the  shop 
in  zero  weather. 

The  floor  foundation  is  formed  of  6  inches  of  concrete  resting  on 
the  natural  soil  well  tamped.  The  concrete  is  composed  of  I  part  Louis- 
ville cement,  2  parts  sand  and  4  parts  stone.  On  the  concrete  are  laid 
yellow  pine  nailing  strips,  3"  x  4",  18  ins.  c.  to  c.,  to  which  is  spiked 
the  I  */$ -in.  splined  hard-maple  flooring.  All  tracks  in  the  shop  are  laid 
with  75~lb.  rails  on  ties  of  New  Mexico  pine  treated  by  the  zinc-chlor- 
ide process,  the  floor  concrete  being  laid  only  to  the  ends  of  the  ties, 
so  that  adjustment  of  the  track  can  be  made  without  tearing  up  the 
floor.  At  the  engine  pits  (which  are  of  concrete)  the  rails  are  laid  on 
longitudinal  timbers.  The  concrete  for  column  foundations  is  com- 
posed of  I  part  lola  Portland  cement,  3  parts  sand  and  5  parts  stone. 
These  foundations  are  8  to  15  ft.  deep,  extending  to  solid  clay.  They 
are  built  up  with  gas  pipe  sleeves  to  form  holes  for  the  anchor  bolts, 
and  the  holes  in  the  bed  plates  of  the  columns  are  slotted  longitudinally 
so  as  to  allow  of  adjustment  for  any  slight  variation.  The  foundations 
for  the  tools,  etc.,  are  also  of  Portland  cement  concrete,  and  these 
are  built  by  the  mechanical  department  to  suit  its  own  requirements  as 
to  arrangement  of  tools.  This  arrangement  was  only  arrived  at  after 
careful  study,  and  of  course  no  changes  can  be  made  without  expen- 
sive work  in  cutting  out  and  replacing  concrete.  One  suggestion  for  the 
floor  construction  was  to  use  a  brick  floor  with  no  concrete,  so  as  to 
allow  for  future  changes  and  putting  in  new  foundations. 


THE  LOCOMOTIVE  ERECTING  AND  MACHINE  SHOP,  PHILADELPHIA  £ 
READING  R.  R.,  READING,  PA.* 

The  combined  machine  and  erecting  shop  is  204  ft.  4^2  ins.  wide 
and  749  ft.  10  ins.  long,  with  provision  made  for  its  extension  to  a 
total  length  of  1,000  ft.  At  its  present  length  it  has  repair  pits  for  70 
locomotives,  and  the  proposed  extension  will  provide  for  30  pits  more. 
Fig.  176  shows  the  general  arrangement  of  the  shop  in  plan,  and  Fig. 
177  is  a  transverse  section  showing  the  general  character  of  the  con- 
struction. 

The  building,  it  will  be  observed,  is  divided  transversely  into  three 
bays  by  means  of  two  rows  of  intermediate  columns  running  lengthwise 
of  the  building.  These  intermediate  columns  and  the  side  wall  columns 
carry  the  roof  trusses  and  the  overhead  cranes,  and  are  spaced  20  ft. 
apart  longitudinally.  The  walls  of  the  building  are  entirely  indepen- 
dent of  the  steelwork.  Considering  the  building  transversely  it  will 
be  observed  that  the  two  side  bays  contain  the  repair  pits ;  one  pit  be- 


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FIG.  176.    PART  PLAN,  SHOWING  PIT  AND  COLUMN  ARRANGEMENT. 

*Engineering  News,  May  24,  1900 


LOCOMOTIVE  ERECTING  SHOP,  PHILADELPHIA  &  READING  R.  R.  373 

tween  each  pair  of  columns,  35  pits  on  each  side  spaced  20  feet  apart 
c.  to  c.  Over  each  side  bay  there  are  two  traveling  crane  tracks, 
one  above  the  other.  The  top  track  will  be  for  a  crane  of  120  tons 
capacity,  capable  of  lifting  a  locomotive  and  carrying  it  the  entire 
length  of  the  building  at  a  height  great  enough  to  clear  the  locomotives 
standing  on  the  repair  pits  beneath.  On  the  lower  track  there  will  be 
placed  a  number  of  35-ton  cranes  for  handling  parts  of  locomotives 
and  material.  The  middle  bay  composes  the  machine  shop,  and  it  is 
also  covered  by  a  track  for  a  number  of  traveling  bridge  cranes  of  10 
tons  capacity  each.  A  material  track  runs  lengthwise  of  the  middle  bay 
at  the  center,  and  for  bringing  the  locomotives  into  the  shop  there  is  a 
track  extending  transversely  through  the  shop  at  each  end.  These 
transverse  tracks  connect  by  means  of  turntables  with  a  yard  track- 
running  parallel  with  the  east  side  of  the  shop. 

Taking  up  the  construction  in  detail,  the  steelwork  is  the  first  part 
perhaps  to  demand  attention.  As  already  stated,  the  nature  and  gen- 
eral arrangement  of  the  steel  frame  is  shown  by  Figs.  176  and  177.  It 
may  be  divided  into  two  parts  for  description.  The  first  part  comprises 


FIG.  177.    TRANSVERSE  SECTION  OF  FRAMEWORK. 

the  main  columns  and  the  traveling  crane  track  system  which  they  sup- 
port directly,  and  the  second  part  comprises  the  roof  framing.  Con- 
sidering the  construction  of  the  main  columns  first,  it  will  be  seen  that 
it  had  to  be  devised  to  withstand  an  unusually  severe  combination  of 
loads,  including  not  only  the  dead  and  wind  loads  usual  to  all  building 
frames,  but  also  a  very  heavy  concentrated  moving  load  from  the  trav- 
eling cranes.  Careful  attention  was  also  required  to  provide  means 
for  longitudinal  expansion  of  the  columns  and  crane  track  girder  sys- 
tem and  still  preserve  the  utmost  stiffness  possible  in  the  heavily  loaded 
crane  tracks. 


374  MISCELLANEOUS  STRUCTURES 

The  interior  and  wall  columns  were  substantially  similar  in  con- 
struction, both  being  composed  of  two  channel  sections  made  up  of 
plates  and  angles,  held  together  by  a  double  lacing  of  2^/2  x  ^2 -in.  bars. 
Fig.  1 80  shows  the  column  construction  in  detail.  Hach  column  is 
founded  on  a  concrete  pier  with  a  granite  capstone.  The  concrete  in 
these  piers  and  for  all  other  foundation  work  was  composed  of  i  part 
Portland  cement,  2  parts  clean  sharp  sand  and  5  parts  stone  broken  to 
pass  a  2-in.  ring.  In  making  the  concrete  the  sand  and  cement  will 
first  be  mixed  dry  and  then  wet,  and  the  wet  mortar  will  then  be  mixed 
with  the  broken  stone  as  it  comes  moist  from  washing.  The  shape  of 
the  column  piers  is  indicated  in  Fig.  177,  and  the  columns  are  fastened 
to  them  by  four  anchor  bolts  for  each  column.  The  columns  are  fin- 
ished by  milling  machine  at  both  top  and  bottom,  and  are  capped  and 
stiffened  at  the  tops  to  provide  a  bearing  for  the  4- ft.  i^-in.  plate 
girders  carrying  the  120-ton  crane  tracks. 

The  track  construction  for  the  bridge  cranes  is  shown  in  detail  in 
Figs.  177  and  180.  As  already  stated,  the  tracks  for  the  I2o-ton  cranes 
are  carried  on  plate  girders  resting  directly  on  the  tops  of  the  columns, 
and  running  lengthwise  of  the  building.  These  track  girders  are  4  ft. 
i%  ins.  deep  back  to  back  of  flange  angles  and  have  spans  of  20  ft., 
c.  to  c.  of  columns.  They  are  milled  square  at  the  ends  and  the  rivets 
of  the  end  angles  have  flat  heads.  To  allow  for  expansion  the  ends  are 
not  butted  close  together,  but  are  separated  by  a  clear  space  of  %-in., 
by  the  construction  shown  in  Fig.  180.  From  the  drawing  it  will  be 
seen  that  each  girder  span  has  one  fixed  and  one  expansion  end,  the 
expansion  being  provided  for  by  the  slotted  rivet  holes  in  the  bearing 
plate  and  by  the  space  between  the  ends  of  the  girders.  An  exactly  simi- 
lar expansion  end  construction  is  provided  for  the  girders  carrying 
the  tracks  for  the  35-ton  and  lo-ton  cranes.  These  three  tracks  are  on 
the  same  level  and  the  girders  supporting  them  are  carried  by  Brackets 
on  the  main  columns.  This  bracket  and  girder  construction  is  shown 
in  Fig.  177. 

The  crane  tracks  proper  consist  of  ordinary  railway  rails  laid  di- 
rectly on  the  special  cover  plate  forming  part  of  the  top  flange  of  each 
track  girder,  to  which  they  are  attached  by  stamped  steel  clips  riveted 
to  the  cover  plate.  For  the  i2O-ton  cranes  the  rails  weigh  150  Ibs.  per 
yard,  for  the  35-ton  cranes  they  weigh  85  Ibs.  per  yard,  and  for  the  10- 
ton  cranes  they  weigh  70  Ibs.  per  yard.  The  joints  are  located  over  the 
expansion  joints  at  each  column  and  are  spaced  ^-in.  open,  the  angle 


LOCOMOTIVE  ERECTING  SHOP,  PHILADELPHIA  &  READING  R.  R.  375 

splices  for  the  rails  being  arranged  to  permit  expansion  and  contrac- 
tion. The  rails  were  rolled  to  the  recommended  Am.  So.  C.  E.  sections 
for  their  respective  weights.  The  specifications  require  that  the  crane 
track  rails  must  be  in  perfect  alinement  horizontally  and  vertically  and 
that  the  gage  must  not  vary  more  than  /4~m-  at  the  maximum.  To 
obtain  vertical  alinement  it  is  specified  that  not  more  than  ^-in.  thick- 
ness of  shims,  each  the  full  size  of  the  bearings,  shall  be  placed  between 
the  column  top  and  the  girder.  The  idea,  it  will  be  seen,  has  been  to 
provide  for  the  heavy  rolling  loads  by  substantial  construction  and  ac- 
curate workmanship,  and  to  keep  the  track  smooth  and  rigid  by  dis- 
tributing the  expansion  over  a  number  of  joints  instead  of  having  all 
the  allowance  made  for  it  at  one  or  two  points. 

Turning  now  to  the  roof  framing,  it  will  be  seen  from  Fig.  177 
that  there  is  a  separate  roof  over  each  longitudinal  bay  of  the  building. 
The  roof  trusses  for  the  middle  bay  rest  directly  on  the  tops  of  the  in- 
termediate rows  of  columns,  but  those  for  the  two  side  bays  are  car- 
ried by  special  roof  columns  rising  from  the  main  columns,  as  shown  by 
Fig.  1 80.  The  trusses  in  each  bay  are  connected  by  purlins  and  lateral 
bracing  and  carry  lantern  roofs  with  glazing.  Details  of  trie  roof  trusses, 
bracing  and  lantern  roof  construction  are  shown  in  Fig.  178  so  fully 
as  to  make  any  further  description  unnecessary.  The  roof  covering  and 
the  glazing  in  the  lanterns,  however,  deserve  brief  special  notice. 

The  roof  covering  consists  first  of  a  I  x  8-in.  hemlock  sheathing, 
having  its  upper  surface  planed.  This  sheathing  is  to  be  covered  by 
four  thicknesses  of  roofing  felt  spread  with  granulated  slag.  The  con- 
struction is  specified  to  be  as  follows:  Make  the  outside  course  next 
the  edge  of  five  thicknesses  of  felt,  then  lay  each  succeeding  layer  at 
least  three-fourths  of  its  width  over  the  preceding  layer,  firmly  securing 
it  in  place,  and  thoroughly  mop  the  surface  underneath  each  succeeding 
layer  as  far  back  as  the  edge  of  the  next  lap  with  a  thin  coating  of  roof- 
ing cement.  This  cement  is  in  no  case  to  be  applied  hot  enough  to  in- 
jure the  wooly  fibre  of  the  felt.  At  least  70  Ibs.  of  felt  must  be  used 
per  loo  sq.  ft.  of  roof.  Over  the  entire  surface  of  the  felt  laid  as  de- 
scribed there  is  to  be  spread  a  good  coating  of  cement,  not  less  than  10 
gallons  (including  what  is  used  between  the  layers  of  felt)  of  cement 
being  employed  per  100  sq.  ft.  of  roof.  This  cement  coating  is  to  be 
covered  with  a  coating  of  slag,  granulated  and  bolted  for  the  purpose, 
using  no  slag  larger  than  will  pass  through  a  ^-in.  mesh  and  none 
smaller  than  will  be  caught  by  a  Y^-\n.  mesh.  This  sJag  must  be  free 


376  MISCELLANEOUS  STRUCTURES 

from  sand,  dust  and  dirt  and  must  be  applied  perfectly  dry  while  the 
cement  is  hot. 

The  structural  features  of  the  glazing  in  the  windows  and  lights 
of  the  monitor  roofs  are  fully  shown  by  the  drawing  of  Figs.  177  and 
178.  It  will  be  noted  that  the  sash  in  the  side  walls  of  the  monitor  roofs 
are  hung  on  pivots  at  the  middle  of  each  side.  There  is  a  similar  ar- 
rangement of  sash  in  the  upper  side  wall  windows  of  the  side  roofs 
overlooking  the  low  middle  roof,  except  that  the  sash  in  alternate  bays 
only  are  pivoted.  These  latter  sash  are  to  be  provided  with  "Brand's" 
sash  openers,  with  chains  operated  from  the  crane  runways  and  ar- 
ranged to  open  all  the  sash  of  one  bay  at  one  time.  The  feature  most 
worthy  of  note,  however,  is  that  the  sash  in  the  side  walls  of  the  moni- 
tor roofs  are  to  be  operated  by  compressed  air  power  from  a  central 
point  on  one  of  the  side  walls  of  the  building  near  the  floor.  The  sash 
will  be  operated  in  sections  about  75  feet  long  and  the  piping  and 
valves  will  be  so  arranged  that  any  one  or  all  of  the  sections  can  be 
operated  at  one  time. 

Next  to  the  framework  of  the  building,  the  structural  features  of 
most  interest  are  perhaps  the  pit  and  floor  construction.  This  is  shown 
in  detail  by  Fig.  180.  In  constructing  the  floor  the  ground  inside 
the  building  will  be  carefully  leveled  and  well  tamped  and  puddled  if 
necessary.  The  entire  area  of  the  main  building,  except  under  the  pits, 
where  cement  concrete  will  be  used,  and  under  the  railway  tracks,  where 
stone  ballast  will  be  used,  will  then  be  covered  with  a  layer  of  bituminous 
concrete.  This  concrete  will  be  composed  of  well  screened  cinders  and 
No.  4  coke  oven  composition  mixed  in  the  proportion  of  at  least  one 
gallon  of  composition  for  each  cubic  foot  of  cinders.  This  composi- 
tion is  to  be  laid  hot  and  well  rammed.  Yellow  pine  floor  sleepers, 
6x6  ins.  square,  will  be  bedded  in  the  bituminous  concrete  at  intervals 
varying  from  4  ft.  to  5  ft.  transversely  of  the  building.  To  these  string- 
ers there  will  be  spiked  an  under  floor,  or  lining,  of  hemlock  plank- 
planed  on  both  edges  and  on  the  upper  side.  On  top  of  this  lining 
there  will  be  laid  a  flooring  of  i*/g  x  4~in.  maple  boards  of  a  uniform 
and  regular  width,  planed  on  top  and  both  edges,  worked  on  the  back 
to  a  depth  of  i-i6-in.  and  a  width  of  2.y^  ins.,  laid  across  hemlock  floor, 
bored  on  a  slant  for  nailing  and  face  nailed  with  I2d.  nails,  the  two 
lines  of  nails  in  each  board  being  staggered.  The  nails  will  be  placed 
in  lines  on  each  side  of  the  board  and  not  over  16  ins.  apart,  and  the 
nails  in  one  line  will  be  opposite  the  middle  point  between  the  nails  in 
the  opposite  line. 


LOCOMOTIVE  ERECTING  SHOP,  PHILADELPHIA  &  READING  R.  R.  377 

The  sidewalls  and  bottoms  of  the  pits  are  made  of  cement  concrete 
of  the  composition  already  described  as  being  employed  in  the  founda- 
tions for  the  main  columns,  Fig.  180,  and  have  a  facing  of  I  in.  of  cem- 
ent. It  will  be  noticed  that  the  bottoms  of  the  pits  are  crowned  trans- 
versely and  have  longitudinal  side  drains  of  "catch  basin"  type,  run- 
ning into  gutters  which  connect  with  the  tile  drain  pipe  system  of  the 
building.  The  pit  rails  are  carried  on  10  x  12-in.  yellow  pine  side  tim- 
bers resting  on  the  concrete  pit  walls  and  connected  By  anchor  rods 
extending  into  the  bituminous  concrete  floor  foundation.  The  railway 
tracks  in  the  building  consist  of  8o-lb.  rails  spiked  to  cross-ties  laid  in 
stone  ballast. 

Before  taking  up  the  exterior  construction  of  the  building,  a  brief 
reference  may  be  made  to  the  method  adopted  for  heating  it.  By  re- 
ferring to  Figs.  176  and  177  it  will  be  noticed  that  an  underground  duct 
extends  along  each  side  of  the  buildings.  This  duct  will  contain  all  the 
steam,  air  and  other  piping  entering  the  building  and  will  also  serve  as 
a  hot-air  duct  for  heating  the  building.  For  the  latter  purpose  the  duct 
connects  with  fan  houses  placed  at  intervals  along  the  side  of  the  build- 
ing, there  being  four  fan  houses  on  the  west  side  and  three  on  the  east 
side.  It  is  expected  that  the  exhaust  steam  will  be  ample  to  heat  the 
building.  The  general  principle  of  the  operation  of  the  heating  appara- 
tus is  to  use  the  air  over  and  over  again,  depending  upon  the  natural  ven- 
tilation to  keep  it  fresh.  Structually  the  ducts  are  simple,  their  bottoms 
and  side  walls  being  of  concrete  with  a  cement  plaster,  and  the  roof  be- 
ing expanded  metal  and  concrete  supported  by  transverse  roof  beams. 
The  roofs  of  the  fan  houses  will  consist  of  I  beams  carrying  T-iron 
purlins  holding  book  tile,  which  in  turn  carry  a  felt  and  slag  roofing 
similar  to  that  already  described  for  the  main  building. 

From  the  structural  point  of  view,  the  wall  construction  of  the 
main  building  presents  nothing  that  is  particularly  notable.  These  walls 
are  of  brick  masonry  resting  on  a  concrete  footing  and  are  anchored  to 
the  wall  columns,  as  shown  by  Fig.  178,  but  they  are  independent  struc- 
tures, receiving  no  support  from  these  columns.  The  entire  wall  area 
is  pretty  well  taken  up  with  doors  and  windows,  there  being  one  in  each 
panel  or  between  each  pair  of  wall  columns.  This  introduces  a  con- 
siderable amount  of  arch  work,  but  nothing  that  is  of  unusual  character. 

To  illustrate  the  simple  methods  which  have  been  adopted  to  secure 
a  pleasing  exterior  appearance  for  the  building,  the  typical  details  of 
the  wall  construction  are  shown  in  Fig.  179. 


378 


MISCELLANEOUS  STRUCTURES 


LOCOMOTIVE  ERECTING  SHOP,  PHILADELPHIA  &  READING  R.  R.    379 


38o 


MISCELLANEOUS  STRUCTURES 


THE  NEW  STEAM  ENGINEERING  BUILDINGS  FOR  THE  BROOKLYN 

NAVY  YARD.* 

The  new  buildings  constructed  for  the  steam  engineering  depart- 
ment of  the  Brooklyn  Navy  Yard,  at  New  York  City,  to  take  the  place 
of  the  buildings  destroyed  by  fire  on  Feb.  15,  1899,  consist  of  a  ma- 
chine shop,  ,an  erecting  shop  and  a  boiler  shop,  arranged  to  occupy  a 
U-shaped  area.  The  erecting  shop  is  130  x  252  ft.,  the  machine  shop 
is  130  x  350  ft.,  and  the  boiler  shop  is  96  x  300  ft. 

The  general  framework  details  of  the  machine,  and  the  erecting 
shops  are  shown  by  Fig.  181.  The  construction  of  the  boiler  shop  is 
similar,  but  the  dimensions  are,  of  course,  smaller.  Referring  to  the 
drawings  of  Fig.  181,  it  will  be  observed  that  the  buildings  are  divided 
transversely  into  three  bays,  a  center  bay  70  ft.  wide  and  two  3O-ft.  side 
bays.  The  two  side  bays  are  covered  by  shed  roofs,  above  which  rise  a 
clerestory  and  gable  roof  to  cover  the  center  bay.  The  side  wall  columns 
are  12-in.  I  beams  filled  between  with  a  brick  wall  for  a  height  of  about 
4  ft.,  and  above  this  point  covered  with  glazing  to  the  cornice  line.  The 
intermediate  columns  are  of  lattice  and  channel  construction,  and  are 
43  ft.  6  ins.  high,  reaching  to  the  level  of  the  junction  of  the  shed  roof 
and  the  clerestory.  They  carry  between  them,  longitudinally  of  the 
buildings  a  double  intersection  truss  15  ft.  deep,  and  support  a  box 
girder  crane  runway  and  the  roof  columns  of  the  clerestory. 

The  framework  is  entirely  of  steel  of  from  60,000  Ibs.  to  70,000 
Ibs.  ultimate  strength,  and  an  elastic  limit  of  one-half  the  ultimate 
strength.  The  specifications  for  workmanship  and  other  essentials 
correspond  to  ordinary  first-class  practice  in  these  respects.  The  no- 
table feature  of  the  building  is  the  extent  to  which  glazing  has  been 
employed  in  the  side  walls  and  roofing,  rather  than  in  any  novelty  in 
the  framework  structure. 

The  foundations  consist  of  concrete  column  pedestals  carried  on 
piles,  the  column  base  plates  being  anchor-bolted  directly  to  the  con- 
crete. The  concrete  used  was  mixed  according  to  the  Navy  Yard 
specifications,  which  require  that  the  cement  exceed  the  voids  in  the 
sand  about  25%,  and  that  the  dry  mixture  of  cement  and  sand  exceeds 

*Engineering  New^s,  April  25,  1901. 


382 


MISCELLANEOUS   STRUCTURES 


the  voids  in  the  aggregate  about  25%.  The  piles  were  driven  to  a 
final  penetration  of  i  in.  under  a  3,ooo-lb.  hammer  falling  15  ft.  The 
usual  requirements  as  to  soundness  of  timber  and  character  of  cement, 
sand,  aggregate  and  water  were  enforced. 

The  side  wall  construction  for  the  shed  bays,  as  already  stated, 
consists  of  a  brick  base  wall  with  glazing  above.    This  glazing  is  put 


FIG.  181.    HALF  TRANSVERSE  SECTION  SHOWING  STEEL  FRAME  DETAILS, 

STEAM  ENGINEERING  BUILDINGS,  BROOKLYN   NAVY  YARD. 


STEAM  ENGINEERING  BUILDINGS,  BROOKLYN  NAVY  YARD     383 

on  in  panels  or  sections ;  each  is  capable  of  being  swung  out  to  provide 
ventilation.  The  side  walls  of  the  clerestory  consist  of  corrugated  iron 
covering  for  the  lower  part,  and  glazing  above.  The  bulk  of  the  area 
of  the  shed  roofs  is  skylight,  and  wide  skylights  are  also  placed  in  the 
clerestory  roof.  Fully  60  per  cent  of  the  area  of  the  external  walls 
and  roof  is  glazed. 

The  large  proportion  of  glazing  to  the  total  wall  and  roof  area 
makes  the  interior  of  the  shops  extremely  well-lighted.  The  entire 
glazing  is  on  the  Paradigm  skylight  and  side  light  system  and  was 
carried  out  by  Arthur  E.  Rendle,  of  New  York  City,  who  controls  the 
system. 

The  entire  construction  is  of  incombustible  materials.  There  is  no 
wood  used  in  the  building,  except  for  the  body  of  the  doors,  and  here 
it  is  covered  with  tin  plate.  In  this  respect,  and  in  respect  to  the  amount 
of  glazing  used,  the  buildings  are  somewhat  remarkable,  even  among 
modern  shop  buildings. 

Turning  now  to  some  of  the  special  details,  it  will  be  noticed  from 
Fig.  181  that  a  somewhat  unusual  construction  has  been  adopted  for  the 
main  columns.  Each  column  consists  of  two  main  members,  each  com- 
posed of  two  channels  riveted  back  to  back,  the  two  main  members  be- 
ing connected  by  double  latticing.  The  resulting  section  is  rather  re- 
markable for  its  length,  as  compared  with  its  width,  but  its  purpose 
was  evidently  to  give  ample  flexural  strength  to  withstand  eccentric  load 
of  the  bridge  crane  girders.  Details  of  the  crane  girders  and  crane 
tracks  are  shown  by  Fig.  181 ;  there  being  one  4O-ton  crane  and  two 
jo-ton  cranes.  It  will  also  be  observed  from  Fig.  181  that  the  lower 
portion  of  the  clerestory  roof  has  a  concrete  and  expanded  metal  cov- 
ering with  roofing  slate  nailed  direct  to  the  concrete.  The  concrete 
is  composed  of  Portland  cement  and  cinder,  and  is  35^  ins.  thick.  The 
floor  construction  throughout  will  be  10  ins.  of  concrete  covered  with 
i  in.  of  granolithic  or  Kosmocrete.  In  the  tool  and  testing  rooms  off 
the  machine  shop,  and  between  the  boiler  and  erecting  shops,  an  effort 
has  been  made  to  secure  a  dust-proof  construction,  and  a  roof  which 
will  be  free  from  drippings  due  to  condensed  moisture.  Over  these 
rooms  the  skylight  roofs  consist  of  double-glazed  Paradigm  skylights, 
with  a  i-in.  air  space  betwen  them. 


PART  SIDE  ELEVATION. 


CBOSS-SECTION  OF  BOILEB  HOUSE. 


I 

GENERAL  CROSS-SECTION  OF  ROLLING  MILL. 


FIG.  182  * 


ROLLING  MILL  BUILDING  FOR  THE  AMERICAN  ROLLING 

MILL  COMPANY,  MIDDLETOWN,  OHIO. 
•Engineering  Record,  July  20,  1901. 


GOVERNMENT  BUILDING,  ST.  Louis  EXPOSITION.* 

The  Government  Building  at  the  St.  Louis  Exposition  had  a  steel 
framework  with  steel  arch  trusses  of  the  three-hinged  type.  The  span 
of  the  arches  is  172  ft.  c.  to  c.  of  pins,  and  their  rise  from  heel  pins  to 
center  pins  is  66  ft.  gl/2  in.  The  trusses  are  spaced  35  ft.  apart,  and 
are  connected  laterally  by  six  lines  of  lattice  girders,  carrying  the 
posts  of  the  main  roof  and  monitor  roof,  and  by  eight  other  intermedi- 
ate transverse  struts.  A  horizontal  wind  strut  truss  is  located  as  shown 
in  Fig.  184. 

The  assumed  loading  was  as  follows :  Dead  Load :  Roof,  10  Ibs. 
per  sq.  ft.  on  slope;  dome,  12  Ibs.  per  sq.  ft.  of  roof  surface;  side 
walls  of  dome  and  building,  15  Ibs.  per  sq.  ft.  of  surface;  trusses,  10 
Ibs.  per  sq.  ft.  of  floor  surface. 

Wind  Load:  Side  walls,  20  Ibs.  per  sq.  ft.;  dome,  curved,  15  Ibs. 
per  sq.  ft.  of  projection  on  a  vertical  surface. 

Snow  Load :  On  roof  of  main  building,  20  Ibs.  per  sq.  ft.  hori- 
zontal ;  reduced  to  10  Ibs.  per  sq.  ft.  on  ventilator  over  center. 

The  revised  estimate  of  loads  for  a  35-ft.  bay  figured  out  as  fol- 
lows, per  sq.  ft.  of  horizontal  projection : 

Lbs.  per  sq.  ft. 

Weight  of  steel  13-1 

"  roof   6.6 

"  tin  covering  .%. 0.5 

Actual  roof  20.2 

Calculated  total  21.5 

The  loading  on  one  truss  for  the  35-ft.  bay  was  : 

Actual  Weight  in  Ibs.  Estimated  Weight  in  Ibs 

Total  Dead  Load 40,500  70,000 

Total  Steel 80,000  64,000 

Grand  Total 120,500  I34,ooo 

The  arches  are  built  up  of  channels,  plates  and  angles,  and  have 
4^2-in.  shoe  pins  and  3~in.  center  pins.  The  shoe  pins  of  each  truss 
are  connected  by  a  tie  bar  consisting  of  a  line  of  9~in.  I-beams.  The 
stresses  in  the  arches  are  given  in  Fig.  183,  while  the  details  are  shown 
in  Fig.  184. 

Engineering  News. 


MISCELLANEOUS  STRUCTURES 


GOVERNMENT  BUILDING 


387 


HorWmd  Truss  \\ 
Seat  for  Yhoden^nsles~"\\  ' 
\±'Bent  Plate  for*  Trus. 
•    Only  ,n  [net  Wings. 


""  t'PtotS  ^^44'fifi 
l'F,lier} 


EMI  Mi»s 


Detail  of  Shoe.1 


A£fl*]ffi9 

p  6,3'Mlers 

FIG.  184.     DETAILS  OF  ARCH. 


Details  of  T>e  Rod, 
End  and  Splice. 


REINFORCED  CONCRETE  ROUND-HOUSE  FOR  THE  CANADIAN   PACIFIC 
RAILWAY  AT  MOOSE  JAW,  CANADA.* 

The  round-house  is  annular  in  plan  and  occupies  a  half  circle,  the 
diameter  of  which  is  350'  5".  The  radial  width  of  the  house  is  80 
feet,  and  it  has  22  stalls  divided  into  two  groups  of  n  stalls  each,  by 
a  radial  fire  wall.  Each  stall  subtends  an  outside  wall  space  of  25'. 


Ts          D».  NEWS. 

FIG.  185.     CROSS  SECTION  OF  REINFORCED  CONCRETE  ROUND-HOUSE. 

The  end  walls,  fire  wall  and  outside  wall  are  of  plain  concrete,  the 
latter  being  enlarged  by  buttresses  or  pilasters  between  stall  spaces 
to  carry  the  outer  ends  of  the  radial  roof  girders,  which  are  further 
supported  by  an  outside  wall  column,  and  two  intermediate  columns. 
The  combined  roof,  wall  and  column  construction  is  shown  in  Fig.  185. 
Each  radial  girder  consists  of  an  18"  @  55  Ibs.  I-beam  encased  in 
concrete  as  shown  in  Fig.  186,  and  is  supported  by  an  outside  wall 
pier  and  three  I-beam  columns  enclosed  in  concrete  as  shown  in  Fig. 
187.  The  space  between  the  main  roof  girders  is  spanned  by  rein- 
forced concrete  beams,  carrying  a  reinforced  roof  slab  and  a  suspended 

•3'Cmcter  Concrete  far  Roof 


qn      _ , . 

Cinder  foncrrte  for  Ceiling 
Sections  of  Concrete  Beam. 


Section  A-B, 

FIG.    186.    CROSS  SECTION  SHOWING  CONSTRUCTION  OF  ROOF  SLABS. 


*  Engineering  News,  February  9,  1905. 


REINFORCED  CONCRETE  ROUND-HOUSE 


— B 


Section    C-D. 


Section    E 


'1  I    X     '»•     A»  •/* 

-p.  ftfftf* 

m 


FIG.  187.  I-BEAM 
COLUMN. 


Sectional      Plan     A-Q. 

FIG.  188.    HOLES  IN  ROOF  FOR  SMOKE  JACK. 


metal  lath  and  plaster  ceiling  as  shown  in  Fig.  186.  The  main  girders 
and  the  angles  which  knee-brace  them  to  the  columns  are  like  the 
columns,  encased  in  concrete.  There  is,  therefore,  no  unprotected 
structural  metal  in  the  round-house. 

The  reinforced  concrete  beams  shown  in  Fig.  186  are  of  uniform 
depth,  but  vary  in  width  and  amount  of  reinforcement  with  the  span 
and  are  composed  of  1-3-5  Portland  cement,  gravel  concrete. 

The  beam  reinforcement  consists  of  plain  rods  attached  to  the 
beams  as  shown  in  Fig.  186.  The  roof  slabs  are  composed  of  cement 
and  washed  cinders,  and  the  ceiling  slab  consists  simply  of  expanded 
metal  wired  to  the  beams  and  given  two  coats  of  cement  plaster,  the 
first  coat  containing  enough  lime  to  make  it  work  well  under  the  trowel, 
and  the  second  coat  being  a  I  cement  to  I  sand  mortar. 


*'/>"                      SJ 
•  O  V  "' P^ 

Part    Side    Elevation.  Cross   Section. 

FIG.  189.    FORMS  FOR  REINFORCED  CONCRETE  ROOF. 


39°  MISCELLANEOUS  STRUCTURES 

It  should  be  noted  that  no  joints  have  been  provided  in  the  roof 
to  accommodate  expansion  and  contraction.  No  cracks  appeared  dur- 
ing the  first  year,  and  none  are  expected  to  appear. 

The  roof  is  reinforced  where  the  metal  smoke  jacks  are  located, 
as  shown  in  Fig.  185  and  Fig.  188. 

The  forms  used  in  constructing  the  roof  are  shown  in  Fig.  189. 
The  round-house  is  standard  for  the  Canadian  Pacific  Railway,  and 
cost  $3,000  per  stall. 


APPENDIX  I. 

GENERAL  SPECIFICATIONS  FOR  STEEL  FRAME 

BUILDINGS. 

BY 

MILO  S.  KETCHUM, 
M.  Am.  Soc.  C.  E. 

SECOND   EDITION. 
1912. 


391 


SPECIFICATIONS  FOR  STEEL  FRAME  BUILDINGS. 

GENERAL  DESCRIPTION. 

1.  Height  of  Building. — The  height  of  the  building  shall  be  the 
distance  from  the  top  of  the  masonry  to  the  under  side  of  the  bottom 
chord  of  the  truss. 

2.  Dimensions  of  Building. — The  width  and  length  of  the  building 
shall  be  the  extreme  distance  out  to  out  of  framing  or  sheathing. 

3.  Length  of  Span. — The  length  of  trusses  and  girders  in  calcu- 
lating stresses  shall  be  considered  as  the  distance  from  center  to  center 
of  end  bearings  when  supported,  and  from  end  to  end  when  fastened 
between  columns  by  connection  angles. 

4.  Pitch  of  Roof. — The  pitch  of  roof  for  corrugated  steel  shall 
preferably  be  not  less  than  \  (6"  in  12"),  and  in  no  case  less  than  £. 
For  a  pitch  less  than  J  some  other  covering  than  corrugated  steel  shall 
be  used. 

5.  Spacing  of  Trusses. — Trusses  shall  be  spaced  so  that  simple 
shapes  may  be  used  for  purlins.     The  spacing  should  be  about  16  feet 
for  spans  of,  say,  -50  feet  and  about  20  to  22  feet  for  spans  of,  say, 
100  feet.     For  longer  spans  than  100  feet  the  purlins  may  be  trussed 
and  the  spacing  may  be  increased. 

6.  Spacing  of  Purlins. — Purlins  shall  be  spaced  not  to  exceed  4'  9" 
where  corrugated  steel  is  used,  and  shall  be  placed  at  panel  points  of 

the  trusses. 

7.  Form  of  Trusses. — The  trusses  shall  preferably  be  of  the  Fink 
type  with  panels  so  subdivided  that  panel  points  will  come  under  the 
purlins.     If  it  is  not  practicable  to  place  the  purlins  at  panel  points,  the 
upper  chords  of  the  trusses  shall  be  designed  to  take  both  the  flexural 
and  direct  stresses.     Trusses  shall  preferably  be  riveted  trusses. 

8.  Bracing. — Bracing  in  the  plane  of  the  lower  chords  shall  be  stiff ; 
bracing  in  the  planes  of  the  top  chords,  the  sides  and  the  ends  may  be 
made  adjustable. 

9.  Proposals. — Contractors   in   submitting  proposals   shall   furnish 
complete  stress  sheets,  general  plans  of  the  proposed  structures  giving 

393 


394 


SPECIFICATIONS. 


sizes  of  material,  and  such  detail  plans  as  will  clearly  show  the  dimen- 
sions of  the  parts,  modes  of  construction  and  sectional  areas. 

10.  Detail    Plans. — The    successful    contractor    shall    furnish    alt 
working  drawings  required  by  the  engineer  free  of  cost.     Working 
drawings  will,  as  far  as  possible,  be  made  on  standard  size  sheets  24" 
X  36"  out  to  out,  2.2."  X34"  inside  the  inner  border  lines. 

11.  Approval  of  Plans. — No  work  shall  be  commenced  or  materials 
ordered  until  the  working  drawings  are  approved  in  writing  by  the 
engineer.     The   contractor   shall   be   responsible    for   dimensions   and 
details  on  the  working  plans,  and  the  approval  of  the  detail  plans  by  the 
engineer  will  not  relieve  the  contractor  of  this  responsibility. 

LOADS. 

12.  The  trusses  shall  be  designed  to  carry  the  following  loads : 

13.  DEAD  LOADS.    Weight  of  Trusses.— The  weight  of  trusses 
per  square  foot  of  horizontal  projection,  up  to  150  feet  span  shall  be 
calculated  by  the  formula 


45 

where  W  =  weight  of  trusses  per  square  foot  of  horizontal  projection; 
P  =  capacity  of  truss  in  pounds  per  square  foot  of  horizontal 

projection; 

L  — span  of  the  truss  in  feet; 
A  =  distance  between  trusses  in  feet. 

14.  Weight  of  Covering.     Corrugated  Steel. — The  weight  of  cor- 
rugated steel  shall  be  taken  from  Table  I. 

TABLE  I. 
WEIGHT  OF  FLAT  AND  CORRUGATED  STEEL  SHEETS  WITH  2|-iNCH  CORRUGATIONS. 


Weight  per  Square  (100  Sq.  Ft.). 

Gage  No. 

Thickness  in 
Inches. 

Flat  Sheets. 

Corrugated  Sheets. 

Black. 

Galvanized. 

Black  Painted. 

Galvanized. 

16 

.0625 

250 

266 

275 

291 

18 

.0500 

200 

216 

220 

236 

20 

•0375 

ISO 

1  66 

165 

182 

22 

•0313 

125 

141 

138 

154 

24 

.0250 

100 

116 

III 

127 

26 

.0188 

75 

9i 

84 

99 

28 

.0156 

63 

79 

69 

86 

STEEL   FRAME    BUILDINGS. 


395 


When  two  corrugations  side  lap  and  six  inches  end  lap  are  used, 
add  25  per  cent  to  the  above  weights;  when  one  corrugation  side  lap 
and  four  inches  end  lap  are  used,  add  15  per  cent  to  the  above  weights 
to  obtain  weight  of  corrugated  steel  laid.  For  paint  add  2  pounds  per 
square.  The  weight  of  covering  shall  be  reduced  to  weight  per  square 
foot  of  horizontal  projection  before  combining  with  the  weight  of 
trusses. 

15.  Slate. — Slate  laid  with  3  inch  lap  shall  be  taken  at  a  weight  of 
7J  pounds  per  square  foot  of  inclined  roof  surface  for  TV'  slate  6" 
X  12",  and  6J  pounds  per  square  foot  of  inclined  roof  surface  for  Ty 
slate  12"  X  24",  and  proportionately  for  other  sizes. 

1 6.  Tile. — Terra-cotta   tile    roofing    weighs    about    6   pounds   per 
square  foot  for  tile  i  inch  thick;  the  actual  weight  of  tile  and  other 
roof  coverings  not  named  shall  be  used. 

17.  Sheathing  and  Purlins. — Sheathing  of  dry  pine  lumber  shall 
be  assumed  to  weigh  3  pounds  per  foot  and  dry  oak  purlins  4  pounds 
per  foot  board  measure. 

1 8.  Miscellaneous  Loads. — The  exact  weight  of  sheathing,  pur- 
lins, bracing,  ventilators,  cranes,  etc.,  shall  be  calculated. 

19.  SNOW  LOADS.— Snow  loads  shall  be  taken  from  the  dia- 
gram in  Fig.  i. 


35  40  45  50 

Latitude  in  Degrees 
FIG.  i.    SNOW  LOAD  ON  ROOFS  FOR  DIFFERENT  LATITUDES,  IN  LBS.  PER  SQUARE  FOOT. 

20.  WIND  LOADS. — The  normal  wind  pressure  on  trusses  shall 
be  computed  by  Duchemin's  formula,  Fig.  2,  with  P  =  3O  pounds  per 
square  foot,  except  for  buildings  in  exposed  locations,  where  P  =  4O 
pounds  per  square  foot  shall  be  used. 
27 


396 


SPECIFICATIONS. 


21.  The  sides  and  ends  of  buildings  shall  be  computed  for  a  normal 
wind  load  of  20  pounds  per  square  foot  of  exposed  surface  for  build- 
ings 30  feet  and  less  to  the  eaves;  30  pounds  per  square  foot  of  exposed 
surface  for  buildings  60  feet  to  the  eaves,  and  in  proportion  for  inter- 
mediate heights. 


O   5    10   15   2O   25   JO   35   4O   45   50.   55   6O   65   TO   75   SO   65   9O 

Angle  Exposed  Roof  mokes  with  Horizontal  in  Degrees ,A. 

FIG.  2.    NORMAL  WIND  LOAD  ON  ROOF  ACCORDING  TO  DIFFERENT  FORMULAS. 

22.  Mine  Buildings. — Mine,  smelter  and  other  buildings  exposed 
to  the  action  of  corrosive  gases  shall  have  their  dead  loads  increased 
25  per  cent. 

23.  Concentrated  Loads. — Concentrated  loads  and  crane  girders 
shall  be  considered  in  determining  dead  loads. 

24.  Purlins. — Purlins  shall  be  designed  to  carry  the  actual  weight 
of  the  covering,  roofing  and  purlins,  but  shall  always  be  designed  for  a 
normal  load  of  not  less  than  30  Ibs.  per  square  foot. 

25.  Girts. — Girts  shall  be  designed  for  a  normal  load  of  not  less 
than  25  Ibs.  per  square  foot. 


STEEL    FRAME    BUILDINGS.  397 

26.  Roof  Covering.  —  Roof  covering  shall  be  designed  for  a  normal 
load  of  not  less  than  30  Ibs.  per  square  foot. 

27.  Minimum  Loads.  —  Xo  roof  shall,  however,  be  designed  for  an 
equivalent  load  of  less  than  30  pounds  per  square  foot  of  horizontal 
projection. 

28.  Loads  on  Foundations.  —  The  loads  on  foundations  shall  not 
exceed  the  following  in  tons  per  square  foot: 

Ordinary  clay  and  dry  sand  mixed  with  clay  .......................     2 

Dry  sand  and  dry  clay  ........................................  •  ----     3 

Hard  clay  and  firm  coarse  sand  ...................................     4 

Firm  coarse  sand  and  gravel  ......................................     5 

Shale  rock   .......................................................     8 

Hard  rock   .......................................................  20 

For  all  soils  inferior  to  the  above,  such  as  loam,  etc.,  never  more  than 
one  ton  per  square  foot. 

29.  Stresses  in  Masonry.  —  The  allowable  stresses  in  masonry  shall 
not  exceed  the  following: 

Tons  per  Lbs.  per 

Sq.  Ft.  Sq.  In. 

Common  brick,  Portland  cement  mortar  ................  12  168 

Hard  burned  brick,  Portland  cement  mortar  ............  15  210 

Rubble  masonry,  Portland  cement  mortar  ..............  10  140 

First  class  masonry,  crystalline  sandstone  or  limestone...  25  350 

First  class  masonry,  granite    ...........................  30  420 

Portland  cement  concrete,  1-3-5   .......................  2°  280 

Portland  cement  concrete,  1-2-4  .......................  30  420 

30.  Pressures  on  Masonry.  —  The  pressure  of  column  bases,  beams, 
etc.,  on  masonry  shall  not  exceed  the  following  in  pounds  per  square 
inch. 

Brick  work  with  cement  mortar  ..................................  250 

Rubble  masonry  with  cement  mortar  .............................  250 

Portland  cement  concrete,  1-2-4  .................................  500 

First  class  dimension  sandstone  or  limestone  ......................  400 

First  class  granite    ..............................................  5°° 

31.  Loads  on  Timber  Piles.  —  The  maximum  load  carried  by  a  pile 
shall  not  exceed  40,000  Ibs.,  or  600  Ibs.  per  sq.  in.  of  its  average  cross- 
section.     The  allowable  load  on  piles  driven  with  a  drop  hammer  shall 


be  determined  by  the  formula  P  =  —  -    .     Where  P  =  safe  load  on 


39$  SPECIFICATIONS. 

pile  in  tons;  W  =  weight  of  hammer  in  tons;  /*  =  free  fall  of  hammer 
in  feet;  s  =  average  'penetration  for  the  last  six  blows  of  the  hammer 
in  inches.  Where  a  steam  hammer  is  used,  TV  is  to  be  used  in  place  of 
unity  in  the  denominator  of  the  right  hand  member  of  the  formula. 

Piles  shall  have  a  penetration  of  not  less  than  10  ft.  in  hard  mate- 
rial, such  as  gravel,  and  not  less  than  15  ft.  in  loam  or  soft  material. 

PROPORTION  OF  PARTS. 

32.  Allowable  Stresses. — In  proportioning  the  different  parts  of 
the  structure  the  maximum  stresses  due  to  the  combinations  of  the 
dead  and  wind  load ;  dead  and  snow  load ;  or  dead,  minimum  snow  and 
wind  load  are  to  be  provided   for.     Concentrated  loads  where  they 
occur  must  be  provided  for. 

33.  Tensile  Stress. — Allowable  Unit  Tensile  Stresses  for  Struc- 
tural Steel.     For  direct  dead,  snow  and  wind  loads. 

Lbs.  per  Sq.  In. 

Shapes,  main  members,  net  section 16,000 

Bars  16,000 

Bottom  flanges  of  rolled  beams 16,000 

Shapes,  laterals,  net  section  20,000 

Iron  rods  for  laterals  20,000 

Plate  girder  webs,  shear  on  net  section 10,000 

Shapes  liable  to  sudden  loading  as  when  used  for 

crane  girders  10,000 

Expansion  rollers  per  lineal  inch 600  X  D 

where  D  =  diameter  of  roller  in  inches. 

Laterals  shall  be  designed  for  the  maximum  stresses  due  to  5,000 
pounds  initial  tension  and  the  maximum  stress  due  to  wind. 

34.  Compressive  Stress. — Allowable  Unit  Compressive  Stress  for 
Structural  Steel.     For  direct  dead,  snow  and  wind  loads 

5  =  1 6,000  —  7O  - 
r 

where  S  =  allowable  unit  stress  in  pounds  per  sq.  in.; 

/=: length  of  member  in  inches  c.  to  c.  of  end  connections; 
r  =  least  radius  of  gyration  of  the  member  in  inches. 

35.  Plate  Girders. — Top  flanges  of  plate  girders   shall  have  the 
same  gross  area  as  the  tension  flanges. 


STEEL   FRAME    BUILDINGS.  399 

36.  Shear  in  webs  of  plate  girders  shall  not  exceed  10,000  pounds 
per  sq.  in.  of  net  section. 

37.  Alternate  Stress. — Members  and  connections  subject  to  alter- 
nate stresses  shall  be  designed  to  take  each  kind  of  stress. 

38.  Combined  Stress. — Members  subject  to  combined  direct  and 
bending   stresses   shall   be   proportioned   according   to   the    following 
formula : 

P         M  v 
S  =  A-    ^ 


where S  =  stress  in  Ibs.  per  sq.  in.  in  extreme  fiber; 
P  =  direct  load  in  Ibs.; 
A  =  area  of  member  in  sq.  in. ; 
M  =  bending  moment  in  in.-lbs. ; 

3(±  =  distance  from  neutral  axis  to  extreme  fiber  in  in. ; 
/  =  moment  of  inertia  of  member; 
/  =  length  member,  or  distance  from  point  of  zero  moment  to 

end  of  member  in  in. ; 
£  —  modulus  of  elasticity  =  30,000,000. 

When  combined  direct  and  flexural  stress  due  to  wind  is  consid- 
ered, 50  per  cent  may  be  added  to  the  above  allowable  tensile  and  com- 
pressive  stresses. 

39.  Stress  Due  to  Weight  of  Member. — Where  the  stress  due  to 
the  weight  of  the  member  or  due  to  an  eccentric  load  exceeds  the 
allowable  stress  for  direct  loads  by  more  than  10  per  cent,  the  section 
shall  be  increased  until  the  total  stress  does  not  exceed  the  above  allow- 
able stress  for  direct  loads  by  more  than  10  per  cent. 

The  eccentric  stress  caused  by  connecting  angles  by  one  leg  when 
used  as  ties  or  struts  shall  be  calculated,  or  only  one  leg  will  be  consid- 
ered effective. 

40.  Rivets. — Rivets  shall  be  so  spaced  that  the  shearing  stress  shall 
not  exceed  11,000  pounds  per  square  inch;  nor  the  pressure  on  the 
bearing  surface  (diameter  X  thickness  of  piece)  of  the  rivet  hole  ex- 
ceed 22,000  pounds  per  square  inch. 

Rivets  in  lateral  connections  may  have  stresses  25  per  cent  in  excess 
of  the  above. 


4OO  SPECIFICATIONS. 

Field  rivets  shall  be  spaced  for  stresses  two  thirds  those  allowed 
for  shop  rivets. 

Field  bolts,  when  allowed,  shall  be  spaced  for  stresses  two  thirds 
those  allowed  for  field  rivets. 

Rivets  and  field  bolts  must  not  be  used  in  direct  tension.  Where  it 
is  necessary  that  connections  take  tension  turned  bolts  shall  be  used. 

41.  Pins. — Pins  shall  be  proportioned  so  that  the  shearing  stress 
shall  not  exceed  11,000  pounds  per  square  inch;  nor  the  pressure  on  the 
bearing  surface  (diameter  X  thickness  of  piece)  of  the  pin  hole  exceed 
22,000  pounds  per  square  inch;  nor  the  extreme  fiber  stress  due  to 
cross  bending  exceed  .24,000  pounds  per  square  inch  when  the  applied 
forces  are  assumed  as  acting  at  the  center  of  the  members. 

42.  Plate   Girders. — Plate   girders    shall   be   proportioned   on   the 
assumption  that  J  of  the  gross  area  of  the  web  is  available  as  flange 
area,  and  the  shear  is  resisted  by  the  web.     The  distance  between  cen- 
ters of  gravity  of  the  flange  areas  shall  be  considered  as  the  effective 
depth  of  the  girder. 

43.  Web  Stiffeners. — The  web  of  plate  girders  shall  have  stiffeners 
•at  the  ends  and  inner  edges  of  bearing  plates,  and  at  points  of  concen- 
trated loads,  and  also  at  intermediate  points  where  the  thickness  of  the 
web  is  less  than  %0  of  the  unsupported  distance  between  flange  angles, 
not  further  apart  than  the  depth  of  the  full  web  plate  with  a  maximum 
limit  of  5  feet.     Stiffeners  shall  be  designed  as  columns  for  a  length 
equal  to  one  half  the  depth  of  the  girder.     Stiffener  angles  must  have 
enough  rivets  to  properly  transmit  the  shear. 

44.  Compression  flanges  of  plate  girders  shall  have  at  least  the 
same  sectional  area  as  the  tension  flanges,  and  shall  not  have  a  stress 

per  sq.  in.  on  the  gross  area  greater  than  16,000 —  I5°^»  where  1  =  un- 
supported distance,  and  b  =  width  of  flange.  Compression  flanges  of 
plate  girders  shall  be  stayed  transversely  when  their  length  is  more 
than  thirty  times  their  width. 

45.  Rolled  Beams. — Rolled  beams  shall  be  proportioned  by  their 
moment  of  inertia.     The  depth  of  rolled  beams  in  floors  shall  not  be 
less  than  %0  of  the  span.     Where  rolled  beams  or  channels  are  used 
as  roof  purlins  the  depths  shall  not  be  less  than  %0  of  the  span. 

46.  Timber. — The  allowable  stresses  in  timber  purlins  and  other 
timbers  shall  be  taken  from  Table  II. 


STEEL   FRAME   BUILDINGS. 


4OI 


TABLE   II. 
ALLOWABLE  WORKING  UNIT  STRESSES,  IN  POUNDS,  PER  SQUARE  INCH. 


Trans- 

She 

ar. 

Kind  of  Timber. 

verse 
Loading', 

End 
Bear- 
ing. 

Under  10 
Diam- 
eters, C 

Bearing 
Across 
Fiber. 

Parallel 
to  Grain. 

Longitu- 
dinal 
Shear  in 
Beams. 

Modulus  of 
Elasticity, 
£ 

White  Oak              

,2OO 

,2OO 

IjOOO 

45O 

2OO 

no 

,  I  SO.OOO 

Long  Leaf  Yellow  Pine... 
White  Pine  and  Spruce  — 
Western  Hemlock. 

,3°° 

,000 

,000 

,300 
,000 
,000 

1,000 
800 
800 

300 
200 
2OO 

1  80 
100 

160 

1  20 
70 

IOO 

,6lO,OOO 
,130,000 

4.80  ooo 

Douglass  Fir  .. 

,200 

,200 

I.OOO 

«o 

180 

no 

.  00,000 

Columns  may  be  used  with  a  length  not  exceeding  45  times  the  least 
dimension.  The  unit  stress  for  lengths  of  more  than  10  times  the  least 
dimension  shall  be  reduced  by  the  following  formula : 

p=c-C-l~ 

100  d 

where C  =  unit  stress,  as  given  above  for  short  columns; 
P==  allowable  unit  stress  in  Ibs.  per  sq.  in.; 
/  =  length  of  column  in  in.; 
d=:  least  side  of  column  in  in. 

COVERING. 

47.  Corrugated  Steel. — Corrugated  steel  shall  generally  have  2j 
inch  corrugations  when  used  for  roof  and  sides  of  buildings,  and  i£ 
inch  corrugations  when  used  for  lining  buildings.     The  minimum  gage 
of  corrugated  steel  shall  be  No.  22  for  roofs,  No.  24  for  sides,  and  No. 
26  for  lining. 

The  gage  of  corrugated  steel  in  U.  S.  standard  gage  and  weight 
per  square  foot  shall  be  shown  on  the  general  plan. 

48.  Spacing  Purlins  and  Girts. — The  span,  or  center  to  center  dis- 
tance of  purlins,  shall  not  exceed  the  distance  given  in  Fig.  3  for  a 
safe  load  of  30  Ibs.  per  sq.  ft.     Corrugated  steel  sheets  shall  prefer- 
ably span  two  purlin  spaces.     Girts  shall  be  spaced  for  a  safe  load  of 
25  Ibs.  per  sq.  ft.  in  Fig.  3. 

49.  End  and  Side  Laps. — Corrugated  steel  shall  be  laid  with  two 
corrugations  side  lap  and  six  inches  end  lap  when  used  for  roofing,  and 
one  corrugation  side  lap  and  four  inches  end  lap  when  used  for  siding. 


402 


SPECIFICATIONS. 


FIG.  3.    SAFE  UNIFORM  LOAD  IN  POUNDS  FOR  CORRUGATED  STEEL  FOR  DIFFERED 

SPANS  IN  FEET. 

50.  Fastening. — Corrugated  steel  shall  be  fastened  to  the  purlins 
and  girts  by  means  of  galvanized  iron  straps  f  inch  wide  by  No.  18 
gage,  spaced  8  to  12  inches  apart;  by  clinch  nails  spaced  8  to  12  inches 
apart;  or  by  nailing  directly  to  spiking  strips  with  8d  barbed  nails, 
spaced  8  inches  apart.     Spiking  strips  shall  preferably  be  used  with 
anti-condensation   lining.     Bolts,   nails   and   rivets   shall    always   pass 
through  the  top  of  corrugations.     Side  laps  shall  be  riveted  with  copper 
or  galvanized  iron  rivets  8  to  12  inches  apart  on  the  roof  and  ij  to  2 
feet  apart  on  the  sides. 

51.  Corrugated  Steel  Lining. — Corrugated  steel  lining  on  the  sides 
shall  be  laid  with  one  corrugation  side  lap  and  four  inches  end  lap. 
Girts  for  corrugated  steel  lining  shall  be  spaced  for  a  safe  load  of  25 
pounds  per  square  foot  as  given  in  Fig.  3. 

52.  Anti-condensation  Lining. — Anti-condensation  roof  lining  shall 
be  used  to  prevent  dripping  in  engine  houses  and  similar  buildings,  and 
shall  be  constructed  as  follows :  Galvanized  wire  poultry  netting  is  fas- 
tened to  one  eave  purlin  and  is  passed  over  the  ridge,  stretched  tight 
and   fastened  to  the  other  eave  purlin.     The  edges  of  the  wire  are 
woven  together  and  the  netting  is  fastened  to  the  spiking  strips,  where 
used,  by  means  of  small  staples.     On  the  netting  are  laid  two  layers  of 
asbestos  paper  TV  in.  thick  and  two  layers  of  tar  paper.     The  corru- 


STEEL   FRAME    BUILDINGS.  403 

gated  steel  is  then  fastened  to  the  purlins  in  the  usual  way;  T3F  in. 
stove  bolts  with  i"  X  i"  X  4"  plate  washers  on  the  lower  side  are  used 
for  fastening  the  side  laps  together  and  for  supporting  the  lining;  or 
the  purlins  may  be  spaced  one  half  the  usual  distance  where  anti- 
condensation  lining  is  used  and  the  stove  bolts  omitted. 

53.  Flashing. — Valleys  or  corners  around  stacks  shall  have  flashing 
extending  at  least  12  inches  above  where  water  will  stand,  and  shall  be 
riveted  or  soldered,  if  necessary,  to  prevent  leakage. 

Flashing  shall  be  provided  above  doors  and  windows. 

54.  Ridge  Roll. — All  ridges  shall  have  a  ridge  roll  securely  fastened 
to  the  corrugated  steel. 

55.  Corner  Finish. — All  corners   shall  be  covered  with  standard 
corner  finish  securely  fastened  to  the  corrugated  steel. 

56.  Cornice. — At  the  gable  ends  the  corrugated  steel  on  the  roof 
shall  be  securely  fastened  to  a  finish  angle  or  channel  connected  to  the 
end  of  the  purlins,  or,  where  molded  cornices  are  used,  to  a  piece  of 
timber  fastened  to  the  ends  of  the  purlins. 

57.  Gutters. — Gutters  and  conductors  shall  be  furnished  at  least 
equal  to  the  requirements  of  the  following  table: 

Span  of  Roof.  Gutter.  Conductor. 

Up       to     50  ft.  6  in.  4  in.  every  40  ft. 

50  ft.  to     70  ft.  7  in.  5  in.  every  40  ft. 

70  ft.  to  100  ft.  8  in.  5  in.  every  40  ft 

Gutters  shall  Lave  a  slope  of  at  least  i  in.  in  15  ft.     Gutters  and 
conductors  shall  be  matle  of  galvanized  steel  not  lighter  than  No.  24. 

58.  Ventilators. — Ventilators  shall  be  provided  and  located  so  as  to 
properly  ventilate  the  building.     They  shall  have  a  net  opening  for 
each  100  square  feet  of  floor  space  as  follows :  not  less  than  one  fourth 
square  foot  for  clean  machine  shops  and  similar  buildings ;  not  less 
than  one  square  foot  for  dirty  machine  shops ;  not  less  than  four  square 
feet  for  mills ;  and  not  less  than  six  square  feet  for  forge  shops,  foun- 
dries and  smelters. 

59.  Shutters  and  Louvres. — Openings  in  ventilators  shall  be  pro- 
vided with  shutters,  sash,  or  louvres,  or  may  be  left  open  as  specified. 

Shutters  must  be  provided  with  a  satisfactory  device  for  opening 
and1  closing. 


4O4  SPECIFICATIONS. 

Louvres  must  be  designed  to  prevent  the  blowing  in  of  rain  and 
snow,  and  must  be  made  stiff  so  that  no  appreciable  sagging  will  occur. 
They  shall  be  made  of  not  less  than  No.  20  gage  galvanized  steel  for 
flat  louvres,  and  No.  24  gage  galvanized  steel  for  corrugated  louvres. 

60.  Circular  Ventilators. — Circular  ventilators,  when  used,  must 
be  designed  so  as  to  prevent  down  drafts.     Net  opening  only  shall  be 
used  in  calculations. 

61.  Windows. — Windows  shall  be  provided  in  the  exterior  walls 
equal  to  not  less  than  10  per  cent  of  the  entire  exterior  surface  in  mill 
buildings,  and  of  not  less  than  25  per  cent  in  machine  shops,  factories, 
washeries,  concentrators,  breakers  and  similar  buildings. 

Window  glass  up  to  12  in.  X  14  in.  may  be  single  strength,  over 
12  in.  X  14  in.  the  glass  shall  be  double  strength.  Window  glass  shall 
be  A  grade  except  in  smelters,  foundries,  forge  shops  and  similar  struc- 
tures, where  it  may  be  B  grade.  The  sash  and  frames  shall  be  con- 
structed of  white  pine.  Where  buildings  are  exposed  to  fire  hazard 
the  windows  shall  have  wire  glass  set  in  metal  sash  and  frames. 

62.  Skylights. — At  least  half  of  the  lighting  shall  preferably  be  by 
means  of  skylights,  or  sash  in  the  sides  of  ventilators. 

Skylights  shall  be  glazed  with  wire  glass,  or  wire  netting  shall  be 
stretched  beneath  the  skylights  to  prevent  the  broken  glass  from  falling 
into  the  building.  Where  there  is  danger  of  the  skylight  glass  being 
broken  by  objects  falling  on  it,  a  wire  netting  guard  shall  be  provided 
on  the  outside. 

Skylight  glass  shall  be  carefully  set,  special  care  being  used  to  pre- 
vent leakage.  Leakage  and  condensation  on  the  inner  surface  of  the 
glass  shall  be  carried  to  the  down-spouts,  or  outside  the  building  by 
condensation  gutters. 

63.  Windows  in  sides  of  buildings  shall  be  made  with  counter- 
balanced sash,  and  in  ventilators  shall  be  made  with  sliding  or  swing 
sash.     All  swinging  windows  shall  be  provided  with  a  satisfactory 
operating  device. 

64.  Doors. — Doors  are  to  be  furnished  as  specified  and  are  to  be 
provided  with  hinges,  tracks,  locks  and  bolts.     Single  doors  up  to  4 
feet  and  double  doors  up  to  8  feet  shall  preferably  be  swung  on  hinges ; 
large  doors,  double  and  single,  shall  be  arranged  to  slide  on  overhead 
tracks,  or  may  be  counterbalanced  to  lift  up  between  vertical  guides. 

Steel  doors  shall  be  firmly  braced  and  shall  be  covered  with  No.  24 
corrugated  steel  with  i^  in.  corrugations. 


STEEL   FRAME    BUILDINGS.  4°5 

The  frames  of  sandwich  doors  shall  be  made  of  two  layers  of  J  in. 
matched  white  pine,  placed  diagonally,  and  firmly  nailed  with  clinch 
nails.  The  frame  shall  be  covered  on  each  side  with  a  layer  of  Xo.  26 
corrugated  steel  with  ij  in.  corrugations.  Locks  and  all  other  neces- 
sary hardware  shall  be  furnished  for  all  windows  and  doors. 

65.  TAR  AND   GRAVEL  ROOF.— Tar  and  gravel   roofs  are 
called  three-,  four-,  five-ply,  etc.,  depending  upon  the  number  of  layers 
of  roofing  felt.     Tar  and  gravel  roofs  may  be  laid  upon  timber  sheath- 
ing or  upon  concrete  slabs. 

66.  Specifications  for  Five-Ply  Tar  and  Gravel  Roof  on  Board 
Sheathing. — The  materials  used  in  making  the  roof  are  I  (one)  thick- 
ness of  sheathing  paper  or  unsaturated  felt,  5   (five)  thicknesses  of 
saturated  felt  weighing  not  less  than  15   (fifteen)  pounds  per  square 
of  one  hundred  (100)  square  feet,  single  thickness,  and  not  less  than 
one  hundred  and  twenty  (120)  pounds  of  pitch,  and  not  less  than  four 
hundred  (400)  pounds  of  gravel  or  three  hundred  (300)  pounds  of  slag 
from  J  to  f  in.  in  size,  free  from  dirt,  per  square  of  one  hundred  ( 100) 
square  feet  of  completed  roof. 

67.  The  material  shall  be  applied  as  follows :  First,  lay  the  sheathing 
or  unsaturated  felt,  lapping  each  sheet  one  inch  over  the  preceding  one. 
Second,   lay  two   (2)   thicknesses  of  tarred   felt,   lapping  each  sheet 
seventeen  (17)  inches  over  the  preceding  one,  nailing  as  often  as  may 
be  necessary  to  hold  the  sheets  in  place  until  the  remaining  felt  is 
applied.     Third,  coat  the  entire  surface  of  this  two-ply  layer  with  hot 
pitch,  mopped  on  uniformly.     Fourth,  apply  three  (3)  thicknesses  of 
felt,  lapping  each  sheet  twenty-two  (22)  inches  over  the  preceding  one, 
mopping  with  hot  pitch  the  full  width  of  the  22  inches  between  the 
plies,  so  that  in  no  case  shall  felt  touch  felt.     Such  nailing  as  is  neces- 
sary shall  be  done  so  that  all  nails  will  be  covered  by  not  less  than  two 
plies  of  felt ;  fifth,  spread  over  the  entire  surface  of  the  roof  a  uniform 
coating  of  pitch,  into  which,  while  hot,  imbed  the  gravel  or  slag.     The 
gravel  or  slag  in  all  cases  must  be  dry. 

68.  Specifications  for  Five-Ply  Tar  and  Gravel  Roof  on  Con- 
crete Sheathing. — The  materials  used  shall  be  the  same  as  for  tar  and 
gravel   roof  on  timber  sheathing,   except  that  the   one  thickness   of 
sheathing  paper  or  unsaturated  felt  may  be  omitted. 

69.  The  materials  shall  be  applied  as  follows :  First,  coat  the  con- 
crete with  hot  pitch,  mopped  on  uniformly.     Second,  lay  two  (2)  thick- 


4O6  SPECIFICATIONS. 

nesses  of  tarred  felt,  lapping  each  sheet  seventeen  (17)  inches  over  the 
preceding  one,  and  mop  with  hot  pitch  the  full  width  of  the  17  inch 
lap,  so  that  in  no  case  shall  felt  touch  felt.  Third,  coat  the  entire  sur- 
face with  hot  pitch,  mopped  on  uniformly.  Fourth,  lay  three  (3) 
thicknesses  of  felt,  lapping  each  sheet  twenty-two  (22)  inches  over  the 
preceding  one,  mopping  with  hot  pitch  the  full  width  of  the  22  inch  lap 
between  the  plies,  so  that  in  no  case  shall  felt  touch  felt.  Fifth,  spread 
the  entire  surface  of  the  roof  with  a  uniform  coat  of  pitch,  into  which, 
while  hot,  imbed  gravel  or  slag. 

70.  SPECIFICATIONS  FOR  CEMENT  FLOOR  ON  A  CON- 
CRETE  BASE.     Materials.— The   cement   used   shall   be   first-class 
Portland  cement,  and  shall  pass  the  standards  of  the  American  Society 
for  Testing  Materials.     The  sand  for  the  top  finish  shall  be  clean  and 
sharp  and  shall  be  retained  on  a  No.  30  sieve  and  shall  have  passed  the 
No.  20  sieve.     Broken  stone  for  the  top  finish  shall  pass  a  J  in.  screen 
and  shall  be  retained  on  the  No.  20  screen.     Dust  shall  be  excluded. 
The  sand  for  the  base  shall  be  clean  and  sharp.     The  aggregate  for  the 
base  shall  be  of  broken  stone  or  gravel  and  shall  pass  a  2  in.  ring. 

71.  Base. — On  a  thoroughly  tamped  and  compacted  subgrade  the 
concrete  for  the  base  shall  be  laid  and  thoroughly  tamped.     The  base 
shall  not  be  less  than  2\  in.  thick.     Concrete  for  the  base  shall  be  thor- 
oughly mixed  with  sufficient  water  so  that  some  tamping  is  required 
to  bring  the  moisture  to  the  surface.     If  old  concrete  is  used  for  the 
base  the  surface  shall  be  roughened  and  thoroughly  cleaned  so  that  the 
new  mortar  will  adhere.     The  roughened  surface  of  old  concrete  shall 
then  be  thoroughly  wet  so  that  the  base  will  not  draw  water  from  the 
finish  when  the  latter  is  applied.     Before  scrubbing  the  base  with  grout 
the  excess  water  shall  be  removed. 

72.  Finish. — With  old  concrete  the  surface  of  the  base  shall  first 
be  scrubbed  with  a  thin  grout  of  pure  cement,  rubbed  in  with  a  broom. 
On  top  of  this,  before  the  thin  coat  is  set,  a  coat  of  finish  mixed  in  the 
proportions  of  one  part  Portland  cement,  one  part  stone  broken  to  pass 
a  \  in.  ring,  and  one  part  sand  shall  be  troweled  on  using  as  much 
pressure  as  possible,  so  that  it  will  take  a  firm  bond.     After  the  finish 
has  been  applied  to  the  desired  thickness  it  should  be  screeded  and 
floated  to  a  true  surface.     Between  the  time  of  initial  and  final  set  it 
shall  be  finished  by  skilled  workmen  with  steel  trowels  and  shall  be 
worked  to  final  surface.     Under  no  condition  shall  a  dryer  be  used, 
nor  shall  water  be  added  to  make  the  material  work  easily. 


STEEL    FRAME    BUILDINGS.  4°  7 

73.  SPECIFICATIONS  FOR  WOOD  FLOOR  ON  A  TAR 
CONCRETE   BASE.     Floor   Sleepers. — Sleepers   for   carrying   the 
timber  floor  shall  be  3  in.  X  3  in.  placed  18  in.  c.  to  c.     After  the  sub- 
grade  has  been  thoroughly  tamped  and  rolled  to  an  elevation  of  4^  in. 
below  the  tops  of  the  sleepers,  the  sleepers  shall  be  placed  in  position 
and  supported  on  stakes  driven  in  the  subgrade.     Before  depositing 
the  tar  concrete  the  sleepers  must  be  brought  to  a  true  level. 

74.  Tar  Concrete  Base. — The  tar  concrete  base  shall  be  not  less 
than  4^  in.  thick  and  shall  be  laid  as  follows:  First,  a  layer  three  (3) 
inches  thick  of  coarse,  screened  gravel  thoroughly  mixed  with  tar,  and 
tamped  to  a  hard  level  surface.     Second,  on  this  bed  spread  a  top 
dressing  ij  inches  thick  of  sand  heated  and  thoroughly  mixed  with 
coal  tar  pitch,  in  the  proportions  of  one  (i)  part  pitch  to  three  (3) 
parts  tar.     The  gravel,  sand  and  tar  shall  be  heated  to  from  200  to 
300  degrees  F.,  and  shall  be  thoroughly  mixed  and  carefully  tamped 
into  place. 

75.  Plank  Sub-Floor. — The  floor  plank  shall  be  of  sound  hemlock 
or  pine  not  less  than  2  inches  thick,  planed  on  one  side  and  one  edge  to 
an  even  thickness  and  width.     The  floor  plank  is  to  be  toe-nailed  with 
4  in.  wire  nails. 

76.  Finished  Flooring. — The  finished  flooring  is  to  be  of  maple  of 
clear  stock,  J  in.  finished  thickness,  thoroughly  air  and  kiln  dried  and 
not  over  4  inches  wide.     The  floor  is  to  be  planed  to  an  even  thickness, 
the  edges  jointed,  and  the  underside  channeled  or  ploughed.     The  fin- 
ished floor  is  to  be  laid  at  right  angles  to  the  sub-floor,  and  each  board 
neatly  fitted  at  the  ends,  breaking  joints  at  random.     The  floor  is  to  be 
final  nailed  with  10  d.  or  3  in.  wire  nails,  nailed  in  diagonal  rows  16 
inches  apart  across  the  boards,  with  two  (2)  nails  in  each  row  in  every 
board.     The  floor  to  be  finished  off  perfectly  smooth  on  completion. 

77.  The  finished  flooring  is  not  to  be  taken  into  the  building  or  laid 
until  the  tar  concrete  base  and  sub-plank  floor  are  thoroughly  dried. 

DETAILS  OF  CONSTRUCTION. 

78.  Details.  —  All   connections   and   details   shall   be   of   sufficient 
strength  to  develop  the  full  strength  of  the  member. 

79.  Pitch  of  Rivets. — The  pitch  of  rivets  shall  not  exceed  6  inches, 
or  sixteen  times  the  thickness  of  the  thinnest  outside  plate  in  the  line 


4O8  SPECIFICATIONS. 

of  stress,  nor  forty  times  the  thickness  of  the  thinnest  outside  plate 
at  right  angles  to  the  line  of  stress.  The  pitch  shall  never  be  less  than 
three  diameters  of  rivet.  At  the  ends  of  compression  members  the 
pitch  shall  not  exceed  four  diameters  of  the  rivet  for  a  length  equal 
to  twice  the  width  of  the  member. 

80.  Edge  Distance. — The  minimum  distance  from  the  center  of 
any  rivet  hole  to  a  sheared  edge  shall  be  ij  in.  for  £  in.  rivets,  ij  in. 
for  f  in.  rivets,  i£  in.  for  f  in.  rivets,  and  I  in.  for  J  in.  rivets,  and 
to  a  rolled  edge  ij,  ij,  I  and  f  in.,  respectively.     The  maximum  dis- 
tance from  the  edge  shall  be  eight  (8)  times  the  thickness  of  the  plate. 

81.  Maximum  Diameter. — The  diameter  of  the  rivets  in  angles 
carrying  calculated  stresses  shall  not  exceed  J  of  the  width  of  the  leg 
in  which  they  are  driven,  except  that  f  in.  rivets  may  be  used  in  2  in. 
angles. 

82.  Diameter  of  Punch  and  Die. — The  diameter  of  the  punch  and 
die  shall  be  as  specified  in  §  147. 

83.  Net  Sections. — The  effective  diameter  of  a  driven  rivet  will  be 
assumed  the  same  as  its  diameter  before  driving.     In  deducting  the 
rivet  holes  to  obtain  net  sections  in  tension  members,  the  diameter  of 
the  rivet  holes  will  be  assumed  as  ^  inch  larger  than  the  undriven  rivet. 

84.  Minimum  Sections. — No  metal   of  less  thickness  than  J   in. 
shall  be  used  except  for  fillers ;  and  no  angles  less  than  2"  X  2"  X  i"- 
The  minimum  thickness  of  metal  in  head  frames,  rock  houses  and  coal 
tipples,  coal  washers  and  coal  breakers  shall  be  ^  inch,  except  for 
fillers.     No  upset  rod  shall  be  less  than  f  in.  in  diameter.     Sag  rods 
may  be  as  small  as  f  in.  diameter. 

85.  Connections. — All  connections  shall  be  of  sufficient  strength  to 
develop  the  full  strength  of  the  member.     No  connections  except  for 
lacing  bars  shall  have  less  than  two  rivets.     All  field  connections  except 
lacing  bars  shall  have  not  less  than  three  rivets. 

86.  Flange  Plates. — The  flange  plates  of  all  girders  shall  not  extend 
beyond  the  outer  line  of  rivets  connecting  them  to  the  angles  more  than 
six  inches  nor  more  than  eight  times  the  thickness  of  the  thinnest  plate. 
87.  Web  Stiffeners. — Web  stiffeners  shall  be  in  pairs,  and  shall 
have  a  close  fit  against  flange  angles.  The  stiffeners  at  the  ends  of 
plate  girders  shall  have  filler  plates.  Intermediate  stiffeners  may  have 
fillers  or  be  crimped  over  the  flange  angles.  The  rivet  pitch  in  stiff- 
eners shall  not  be  greater  than  5  inches. 


STEEL    FRAME    BUILDINGS.  409 

88.  Web  Splices. — Web  plates  shall  be  spliced  at  all  points  by  a 
plate  on  each  side  of  the  web,  capable  of  transmitting  the  shearing  and 
bending  stresses  through  the  splice  rivets. 

89.  Net  Sections. — Net  sections  must  be  used  in  calculating  ten- 
sion members  and  in  deducting  the  rivet  holes  they  shall  be  taken  -J  in. 
larger  than  the  nominal  size  of  rivet. 

90.  Pin  connected  riveted  tension  members  shall  have  a  net  section 
through  the  pin  hole  25  per  cent  in  access  of  the  required  net  section 
of  the  member.     The  net  section  back  of  the  pin  hole  in  line  of  the 
center  of  the  pin  shall  be  at  least  0.75  of  the  net  section  through  the 
pin  hole. 

91.  Upset  Rods. — All  rods  with  screw  ends,  except  sag  rods,  must 
be  upset  at  the  ends  so  that  the  diameter  at  the  base  of  the  threads  shall 
be  TV  mcn  larger  than  any  part  of  the  body  of  the  bar. 

92.  Upper  Chords. — Upper  chords  of  trusses  shall  have  symmet- 
rical cross-sections,  and  shall  preferably  consist  of  two  angles  back 
to  back. 

93.  Compression  Members. — All  other  compression  members  for 
roof  trusses,  except  sub-struts,  shall  be  composed  of  sections  symmet- 
rically placed.     Sub-struts  may  consist  of  a  single  section. 

94.  Columns. — Side  posts  which  take  flexure  shall  preferably  be 
composed  of  4  angles  laced,  or  4  angles  and  a  plate.     Where  side  posts 
do  not  take  flexure  and  carry  heavy  loads  they  shall  preferably  be  com- 
posed of  two  channels  laced,  or  of  two  channels  with  a  center  diaphragm. 

95.  Posts  in  end  framing  shall  preferably  be  composed  of  I-beams 
or  4  angles  laced.     Corner  columns  shall  preferably  be  composed  of 
one  angle. 

96.  Crane  Posts. — The  cross-bending  stress  due  to  eccentric  load- 
ing in  columns  carrying  cranes  shall  be  calculated.     Crane  girders  car- 
rying heavy  cranes  shall  be  carried  on  independent  columns. 

97.  Batten  Plates. — Laced  compression  members  shall  be  stayed  at 
the  ends  by  batten  plates,  placed  as  near  the  end  of  the  member  as 
practicable  and  having  a  length  not  less  than  the  greatest  width  of  the 
member.     The  thickness  of  batten  plates  shall  not  be  less  than  %0  of 
the  distance  between  rivet  lines  at  right  angles  to  axis  of  member. 

98.  Lacing. — Single  lacing  bars  shall  have  a  thickness  of  not  less 
than  y±Q,  and  double  bars  connected  by  a  rivet  at  the  intersection  of 
not  less  than  %0  °f  the  distance  between  the  rivets  connecting  them  to 


4IO  SPECIFICATIONS. 

the  member;  they  shall  make  an  angle  not  less  than  45  degrees  with 
the  axis  of  the  member ;  their  width  shall  be  in  accordance  with  the  fol- 
lowing standards,  generally: 

Size  of  Member.  Width  of  Lacing  Bars. 

For  15  inch  channels,  or  built  sections  with) 

,        ,      .     ,          .  }•  2%  inches  (I  inch  rivets). 

3^  and  4  inch  angles.  j 

For  12,  10,  o  inch  channels,  or  built  sections') 

...       .     ,  \  2\  inches  (f  inch  rivets), 

with  3  inch  angles.  J 

For  8  and  7  inch  channels,  or  built  sections') 

.,/.,.  [•  2  inches  (f  inch  rivets). 

with  2\  inch  angles.  j 

For  6  and  5  inch  channels,  or  built  sections")     . 

.. .       :    ,  \\\  inches  (\  inch  rivets), 

with  2  inch  angles.  j 

Where  laced  members  are  subjected  to  bending,  the  size  of  lacing 
bars  or  angles  shall  be  calculated,  or  a  solid  web  plate  shall  be  used. 

99.  Pin  Plates. — All  pin  holes   shall  be  reinforced  by  additional 
material  when  necessary,  so  as  not  to  exceed  the  allowable  pressure  on 
the  pins.     These  reinforcing  plates  must  contain  enough  rivets  to  trans- 
fer the  proportion  of  pressure  which  comes  upon  them,  and  at  least 
one  plate  on  each  side  shall  extend  not  less  than  6  inches  beyond  the 
edge  of  the  batten  plate. 

100.  Maximum  Length  of  Compression  Members. — No  compres- 
sion member  shall  have  a  length  exceeding  125  times  its  least  radius  of 
gyration  for  main  members,  nor  150  times  its  least  radius  of  gyration 
for  laterals  and  sub-members.     The  length  of  a  main  tension  member 
in  which  the  stress  is  reversed  by  the  wind  shall  not  exceed  150  times 
its  least  radius  of  gyration. 

101.  Maximum  Length  of  Tension  Members. — The  length  of  riv- 
eted tension  members  in  horizontal  or  inclined  position  shall  not  exceed 
200  times  their  radius  of  gyration  except  for  wind  bracing,  which  mem- 
bers may  have  a  length  equal  to  250  times  the  least  radius  of  gyration. 
The  horizontal  projection  of  the  unsupported  portion  of  the  member 
is  to  be  considered  the  effective  length. 

102.  Splices. — In  compression  members  joints  with  abutting  faces 
planed  shall  be  placed  as  near  the  panel  points  as  possible,  and  must  be 
spliced  on  all  sides  with  at  least  two  rows  of  rivets  on  each  side  of  the 
joint.    Joints  with  abutting  faces  not  planed  must  be  fully  spliced. 


STEEL   FRAME    BUILDINGS.  411 

103.  Splices. — Joints  in  tension  members  shall  be  fully  spliced. 

104.  Tension    Members. — Tension    members    shall   preferably   be 
composed  of  angles  or  shapes  capable  of  taking  compression  as  well  as 
tension.     Flats  riveted  at  the  ends  shall  not  be  used. 

105.  Main  tension  members  shall  preferably  be  made  of  2  angles, 
2  angles  and  a  plate,  or  2  channels  laced.     Secondary  tension  members 
may  be  made  of  a  single  shape. 

106.  Eye-Bars. — Heads  of  eye-bars  shall  be  so  proportioned  as  to 
develop  the  full  strength  of  the  bar.     The  heads  shall  be  forged  and 
not  welded. 

107.  Pins. — Pins  must  be  turned  true  to  size  and  straight,  and  must 
be  driven  to  place  by  means  of  pilot  nuts. 

The  diameter  of  pin  shall  not  be  less  than  f  of  the  depth  of  the 
widest  bar  attached  to  it. 

The  several  members  attached  to  a  pin  shall  be  packed  so  as  to 
produce  the  least  bending  moment  on  the  pin,  and  all  vacant  spaces 
must  be  filled  with  steel  or  cast  iron  fillers. 

108.  Bars  or  Rods. — Long  laterals  may  be  made  of  bars  with  clevis 
or  sleeve  nut  adjustment.     Bent  loops  shall  not  be  used. 

109.  Spacing  Trusses. — Trusses  shall  preferably  be  spaced  so  as  to 
allow  the  use  of  single  pieces  of  rolled  sections  for  purlins.     Trussed 
purlins  shall  be  avoided  if  possible. 

no.  Purlins  and  Girts. — Purlins  and  girts  shall  preferably  be  com- 
posed of  single  sections — channels,  angles  or  Z-bars,  placed  with  web 
at  right  angles  to  the  trusses  and  posts  and  legs  turned  down. 

in.  Fastening. — Purlins  and  girts  shall  be  attached  to  the  top 
chord  of  trusses  and  to  columns  by  means  of  angle  clips  with  two  rivets 
in  each  leg. 

112.  Spacing. — Purlins  for  corrugated  steel  without  sheathing  shall 
be  spaced  at  distances  apart  not  to  exceed  the  span  as  given  for  a  safe 
load  of  30  pounds,  and  girts  for  a  safe  load  of  25  pounds  as  given 
in  Fig.  3. 

113.  Timber  Purlins. — Timber  purlins  and  girts  shall  be  attached 
and  spaced  the  same  as  steel  purlins. 

114.  Base  Plates. — Base  plates  shall  never  be  less  than  \  inch  in 
thickness,  and  shall  be  of  sufficient  thickness  and  size  so  that  the  pres- 
sure on  the  masonry  shall  not  exceed  the  allowable  pressures  in  §  30. 

28 


4I2 


SPECIFICATIONS. 


115.  Anchors. — Columns  shall  be  anchored  to  the  foundations  by 
means  of  two  anchor  bolts  not  less  than  i  in.  in  diameter  upset,  placed 
as  wide  apart  as  practicable  in  the  plane  of  the  wind.     The  anchorage 
shall  be  calculated  to  resist  one  and  one  half  times  the  bending  moment 
at  the  base  of  the  columns. 

1 1 6.  Lateral  Bracing. — Lateral  bracing  shall  be  provided  in  the 
plane  of  the  top  and  bottom  chords,  sides  and  ends ;  knee  braces  in  the 
transverse  bents ;  and  sway  bracing  wherever  necessary.     Lateral  brac- 
ing shall  be  designed  for  an  initial  stress  of  5,000  pounds  in  each  mem- 
ber, and  provision  must  be  made  for  putting  this  initial  stress  into  the 
members  in  erecting. 

117.  Temperature. — Variations  in  temperature  to  the  extent  of  150 
degrees  F.  shall  be  provided  for. 

MATERIAL  AND  WORKMANSHIP. 
MATERIAL. 

1 1 8.  Process  of  Manufacture. — Steel  shall  be  made  by  the  open- 
hearth  process. 

119.  Schedule  of  Requirements. 


Chemical  and  Physical 
Properties. 

Structural  Steel. 

Rivet  Steel. 

Steel  Castings. 

Phosphorus  Max..  |  ^C  - 
Sulphur  maximum               . 

0.04  per  cent. 
0.08  •«      " 
o.o";  "     " 

o.oj.  per  cent. 
0.04    "      " 
0  04.     "       " 

0.05  per  cent. 
0.08    "       •• 
0.05    "      " 

Ultimate  tensile  strength.. 
Pounds  per  square  inch  

Desired 
60,000 
1,500,000* 

Desired 
50,000 
1,500,000 

Not  less  than 
65,000 

Elongation:  min.  %  in  2/x... 
Character  of  fracture 

Ult.  tensile  strength 

22 

Silky 

Ult.  tensile  strength. 
Silky 

18 

Silky  or  fine  granular 

Cold  bends  without  fracture. 

1  80°  flatt 

1  80°  flatt 

90°,  d  =  3/ 

The  yield  point,  as  indicated  by  the  drop  of  beam,  shall  be  recorded 
in  the  test  reports. 

1 20.  Allowable  Variations. — If  the  ultimate  strength  varies  more 
than  4,000  Ibs.  from  that  desired,  a  retest  shall  be  made  on  the  same 


*  See  paragraph  128. 

f  See  paragraphs  129,  130  and  131. 

$  See  paragraph  132. 


STEEL   FRAME    BUILDINGS. 


413 


gage,  which,  to  be  acceptable,  shall  be  within  5,000  Ibs.  of  the  desired 
ultimate. 

121.  Chemical    Analyses. — Chemical    determinations   of   the   per- 
centages of  carbon,  phosphorus,  sulphur  and  manganese  shall  be  made 
by  the  manufacturer  from  a  test  ingot  taken  at  the  time  of  the  pouring 
of  each  melt  of  steel  and  a  correct  copy  of  such  analysis  shall  be  fur- 
nished to  the  engineer  or  his  inspector.     Check  analyses  shall  be  made 
from  finished  material,  if  called  for  by  the  purchaser,  in  which  case  an 
excess  of  25  per  cent  above  the  required  limits  will  be  allowed. 

122.  Form  of   Specimens.     PLATES,   SHAPES  AND   BARS. — Speci- 
mens for  tensile  and  bending  tests  for  plates,  shapes  and  bars  shall  be 
made  by  cutting  coupons  from  the  finished  product,  which  shall  have 
both  faces  rolled  and  both  edges  milled  to  the  form  shown  by  Fig.  I ; 
or  with  both  edges  parallel ;  or  they  may  be  turned  to  a  diameter  of  f 
inch  for  a  length  of  at  least  9  inches,  with  enlarged  ends. 

123.  RIVETS. — Rivet  rods  shall  be  tested  as  rolled. 

124.  PINS  AND  ROLLERS. — Specimens  shall  be  cut  from  the  finished 
rolled  or  forged  bar,  in  such  manner  that  the  center  of  the  specimen 
shall  be  I  inch  from  the  surface  of  the  bar.     The  specimen  for  tensile 
test  shall  be  turned  to  the  form  shown  by  Fig.  2.     The  specimen  for 
bending  test  shall  be  i  inch  by  ^  inch  in  section. 


Parallel  Section 


E 


Not  less  than  9"  f  B 


Abput  a1 


K**!*****,  u 

— About1 18 

FIG.  i 


FIG.  2 


125.  STEEL  CASTINGS. — The  number  of  tests  will  depend  on  the 
character  and  importance  of  the  castings.  Specimens  shall  be  cut  cold 
from  coupons  molded  and  cast  on  some  portion  of  one  or  more  castings 
from  each  melt  or  from  the  sink  heads,  if  the  heads  are  of  sufficient 


414  SPECIFICATIONS. 

size.  The  coupon  or  sink  head,  so  used,  shall  be  annealed  with  the 
casting  before  it  is  cut  off.  Test  specimens  shall  be  of  the  form  pre- 
scribed for  pins  and  rollers. 

126.  Annealed  Specimens. — Material  which  is  to  be  used  without 
annealing  or  further  treatment  shall  be  tested  in  the  condition  in  which 
it  comes  from  the  rolls.     When  material  is  to  be  annealed  or  otherwise 
treated  before  use,  the  specimens  for  tensile  tests  representing  such 
material  shall  be  cut  from  properly  annealed  or  similarly  treated  short 
lengths  of  the  full  section  of  the  bar. 

127.  Number  of  Tests. — At  least  one  tensile  and  one  bending  test 
shall  be  made  from  each  melt  of  steel  as  rolled.     In  case  steel  differing 
f  in.  and  more  in  thickness  is  rolled  from  one  melt,  a  test  shall  be  made 
from  the  thickest  and  thinnest  material  rolled. 

128.  Modifications  in  Elongation. — For  material  less  than  -f$  in. 
and  more  than  f  in.  in  thickness  the  following  modifications  will  be 
allowed  in  the  requirements  for  elongation : 

(a)  For  each  TV  in.  in  thickness  below  -f^  in.,  a  deduction  of  2-J 
per  cent  will  be  allowed  from  the  specified  elongation. 

(I)  For  each  %  in.  in  thickness  above  f  in.,  a  deduction  of  I  per 
cent  will  be  allowed  from  the  specified  elongation. 

(c)  For  pins  and  rollers  over  3  in.  in  diameter  the  elongation  in 
8  in.  may  be  5  per  cent  less  than  that  specified  in  paragraph  119. 

129.  Bending  Tests. — Bending  tests  may  be  made  by  pressure  or 
by  blows.     Plates,  shapes  and  bars  less  than  I  in.  thick  shall  bend  as 
called  for  in  paragraph  119. 

130.  'Thick  Material. — Full-sized  material  for  eye-bars  and  other 
steel  i  in.  thick  and  over,  tested  as  rolled,  shall  bend  cold  180  degrees 
around  a  pin  the  diameter  of  which  is  equal  to  twice  the  thickness  of 
the  bar,  without  fracture  on  the  outside  of  bend. 

131.  Bending  Angles. — Angles  j  in.  and  less  in  thickness  shall  open 
flat  and  angles  -J  in.  and  less  in  thickness  shall  bend  shut,  cold,  under 
blows  of  a  hammer,  without  sign  of  fracture.     This  test  will  be  made 
only  when  required  by  the  inspector. 

132.  Nicked  Bends. — Rivet  steel,  when  nicked  and  bent  around  a 
bar  of  the  same  diameter  as  the  rivet  rod,  shall  give  a  gradual  break 
and  a  fine,  silky,  uniform  fracture. 

133.  Finish, — Finished  material  shall  be  free  from  injurious  seams, 
flaws,  cracks,  defective  edges,  or  other  defects,  and  have  a  smooth, 


STEEL   FRAME    BUILDINGS. 


415 


uniform,  workmanlike  finish.     Plates  36  in.  in  width  and  under  shall 
have  rolled  edges. 

134.  Stamping. — Every  finished  piece  of  steel  shall  have  the  melt 
number  and  the  name  of  the  manufacturer  stamped  or  rolled  upon  it. 
Steel  for  pins  and  rollers  shall  be  stamped  on  the  end.     Rivet  and 
lattice  steel  and  other  small  parts  may  be  bundled  with  the  above  marks 
on  an  attached  metal  tag. 

135.  Defective  Material. — Material  which,  subsequent  to  the  above 
tests  at  the  mills,  and  its  acceptance  there,  develops  weak  spots,  brit- 
tleness,  cracks  or  other  imperfections,  or  is   found  to  have  injurious 
defects,  will  be  rejected  at  the  shop  and  shall  be  replaced  by  the  manu- 
facturer at  his  own  cost. 

136.  Allowable  Variation  in  Weight. — A  variation  in  cross-section 
or  weight  of  each  piece  of  steel  of  more  than  2.\  per  cent  from  that 
specified  will  be  sufficient  cause  for  rejection,  except  in  case  of  sheared 
plates,  which  will  be  covered  by  the  following  permissible  variations, 
which  are  to  apply  to  single  plates. 

137.  When  Ordered  to  Weight. — Plates  12 J  pounds  per  square 
foot  or  heavier : 

(a)  Up  to  100  in.  wide,  2j  per  cent  above  or  below  the  pre- 
scribed weight. 

PLATES  Y±  INCH  AND  OVER  IN  THICKNESS. 


Width  of  Plate. 

Ordered. 

Weight. 

Up  to  75  Inch. 

75"  and  up  to 
loo". 

100"  and  up  to 
115." 

Over  115." 

1-4  inch. 

io.2olbs.     j   10     percent. 

14    per  cent. 

1  3     per  cent. 

5-16 

12.75 

8 

12 

16 

3-8 

I5-30 

7 

10 

13 

17  per  cent. 

7-16 

17-85 

6 

8 

10 

13 

« 

1-2 

20.40 

c 

7 

9 

12 

« 

9-l6 

22.95 

4^ 

6^ 

W 

II 

(( 

5-8 

25-5° 

4 

6 

8 

10 

K 

Over  5-8 

3% 

5 

6y2 

9 

« 

PLATES  UNDER  y±  INCH  ix  THICKNESS. 


Width  of  Plate. 


Ordered. 

LJS.  per  Square  Ft. 

Up  to  50." 

50"  and  up  to 
70" 

Over  70." 

1-8  »  up  to  5-32" 
5-32     "   "3-16 
3_!6     «  "  1-4 

5.10  to    6.37 
6.37    "      7.65 
7.65    "   IO.2O 

10      per  cent. 

«*?  :; 

15      per  cent. 
I2i/  «<      « 

10         "         " 

20  per  cent. 
17     "       " 
15     "       " 

41 6  SPECIFICATIONS. 

(b)   One  hundred  in.  wide  and  over,  5  per  cent  above  or  below 

138.  Plates  under  12^  pounds  per  square  foot: 

(a)  Up  to  75  in.  wide,  2^  per  cent  above  or  below. 

(b)  Seventy-five  in.  and  up  to  100  in.  wide,  5  per  cent  above  or 
3  per  cent  below. 

(c)  One  hundred  in.  wide  and  over,  10  per  cent  above  or  3  per 
cent  below. 

139.  When  Ordered  to  Gage. — Plates  will  be  accepted  if  they 
measure  not  more  than  .01  inch  below  the  ordered  thickness. 

140.  An   excess   over   the   nominal   weight,    corresponding   to   the 
dimensions  on  the  order,  will  be  allowed  for  each  plate,  if  not  more 
than  that  shown  in  the  preceding  tables,  one  cubic  inch  of  rolled  steel 
being  assumed  to  weigh  0.2833  pounds. 

SPECIAL  METALS. 

141.  Cast-Iron. — Except  where  chilled  iron  is  specified,  castings 
shall  be  made  of  tough  gray  iron,  with  sulphur  not  over  o.io  per  cent. 
They  shall  be  true  to  pattern,  out  of  wind  and  free  from  flaws  and 
excessive  shrinkage.     If  tests  are  demanded  they  shall  be  made  on  the 
"Arbitration   Bar"  of  the  American   Society   for  Testing  Materials, 
which  is  a  round  bar,  ij  in.  in  diameter  and  15  in.  long.     The  trans- 
verse test  shall  be  on  a  supported  length  of  12  in.  with  load  at  middle. 
The  minimum  breaking  load  so  applied  shall  be  2,900  Ibs.,  with  a  deflec- 
tion of  at  least  -f$  inch  before  rupture. 

142.  Wrought-Iron   Bars. — Wronght-iron   shall   be   double-rolled, 
tough,  fibrous  and  uniform  in  character.     It  shall  be  thoroughly  welded 
in  rolling  and  be  free  from  surface  defects.     When  tested  in  specimens 
of  the  form  of  Fig.  I,  or  in  full-sized  pieces  of  the  same  length,  it  shall 
show  an  ultimate  strength  of  at  least  50,000  Ibs.  per  sq.  in.,  an  elonga- 
tion of  at  least  18  per  cent  in  8  in.,  with  fracture  wholly  fibrous.    Speci- 
mens shall  bend  cold,  with  the  fiber  through   135°,  without  sign  of 
fracture,  around  a  pin  the  diameter  of  which  is  not  over  twice  the 
thickness  of  the  piece  tested.     When  nicked  and  bent  the  fracture  shall 
show  at  least  90  per  cent  fibrous. 

WORKMANSHIP. 

143.  General. — All  parts  forming  a  structure  shall  be  built  in  ac- 
cordance with  approved  drawings.     The  workmanship  and  finish  shall 
be  equal  to  the  best  practice  in  modern  bridge  works. 


STEEL   FRAME    BUILDINGS. 

144.  Straightening  Material. — Material  shall  be  thoroughly  straight- 
ened in  the  shop,  by  methods  that  will  not  injure  it,  before  being  laid 
off  or  worked  in  any  -way 

145.  Finish. — Shearing  shall  be  neatly  and  accurately  done  and  all 
portions  of  the  work  exposed  to  view  neatly  finished. 

146.  Rivets. — The  size  of  rivets,  called  for  on  the  plans,  shall  be 
understood  to  mean  the  actual  size  of  the  cold  rivet  before  heating. 

147.  Rivet   Holes. — When  general   reaming  is   not  required,  the 
diameter  of  the  punch  for  material  not  over  f  in.  thick  shall  be  not 
more  than  TV  in->  nor  tnat  °f  the  die  more  than  -J  in.  larger  than  the 
diameter  of  the  rivet.     The  diameter  of  the  die  shall  not  exceed  that 
of  the  punch  by  more  than  J  the  thickness  of  the  metal  punched. 

148.  Planing  and  Reaming. — In  medium  steel  over  f  of  an  in.  thick, 
all  sheared  edges  shall  be  planed  and  all  holes  shall  be  drilled  or  reamed 
to  a  diameter  of  -J  of  an  in.  larger  than  the  punched  holes,  so  as  to 
remove  all  the  sheared  surface  of  the  metal.     Steel  which  does  not 
satisfy  the  drifting  test  must  have  holes  drilled. 

149.  Punching. — Punching  shall  be  accurately  done.     Slight  inac- 
curacy in  the  matching  of  holes  may  be  corrected  with  reamers.    Drift- 
ing to  enlarge  unfair  holes  will  not  be  allowed.     Poor  matching  of 
holes  will  be  cause  for  rejection  by  the  inspector. 

150.  Assembling. — Riveted    members    shall    have    all    parts    well 
pinned  up  and  firmly  drawn  together  with  bolts  before  riveting  is  com- 
menced.    Contact  surfaces  to  be  painted  (see  §  182). 

151.  Lacing  Bars.— Lacing  bars  shall  have  neatly  rounded  ends, 
unless  otherwise  called  for. 

152.  Web  Stiff eners. — Stiff eners  shall  fit  neatly  between  flanges  of 
girders.     Where  tight  fits  are  called  for  the  ends  of  the  stiffeners  shall 
be  faced  and  shall  be  brought  to  a  true  contact  bearing  with  the  flange 
angles. 

153.  Splice  Plates  and  Fillers. — Web  splice  plates  and  fillers  under 
stiffeners  shall  be  cut  to  fit  within  -J  in.  of  flange  angles. 

154.  Web  Plates. — Web  plates  of  girders,  which  have  no  cover 
plates,  shall  be  flush  with  the  backs  of  angles  or  be  not  more  than  J  in. 
scant,  unless  otherwise  called  for.     When  web  plates  are  spliced,  not 
more  than  J  in.  clearance  between  ends  of  plates  will  be  allowed. 

155.  Connection  Angles. — Connection  angles  for  girders  shall  be 
flush  with  each  other  and  correct  as  to  position  and  length  of  girder. 


4 1 8  SPECIFICATIONS. 

In  case  milling  is  required  after  riveting,  the  removal  of  more  than  TV 
in.  from  their  thickness  will  be  cause  for  rejection. 

156.  Riveting. — Rivets  shall  be  driven  by  pressure  tools  wherever 
possible.     Pneumatic  hammers  shall  be  used  in  preference  to  hand 
driving. 

157.  Rivets  shall  look  neat  and  finished,  with  heads  of  approved 
shape,  full  and  of  equal  size.     They  shall  be  central  on  shank  and  grip 
the  assembled  pieces  firmly.     Recupping  and  calking  will  not  be  allowed. 
Loose,  burned  or  otherwise  defective  rivets  shall  be  cut  out  and  re- 
placed.    In  cutting  out  rivets  great  care  shall  be  taken  not  to  injure 
the  adjacent  metal.     If  necessary  they  shall  be  drilled  out. 

158.  Turned  Bolts. — Wherever  bolts  are  used  in  place  of  rivets 
which  transmit  shear,  the  holes  shall  be  reamed  parallel  and  the  bolts 
turned  to  a  driving  fit.     A  washer  not  less  than  J  in.  thick  shall  be  used 
under  nut. 

159.  Members  to  be  Straight. — The  several  pieces  forming  one 
built  member  shall  be  straight  and  fit  closely  together,  and  finished 
members  shall  be  free  from  twists,  bends  or  open  joints. 

1 60.  Finish  of  Joints. — Abutting  joints  shall  be  cut  or  dressed  true 
and  straight  and  fitted  close  together,  especially  where  open  to  view. 
In  compression  joints  depending  on  contact  bearing  the  surfaces  shall 
be  truly  faced,  so  as  to  have  even  bearings  after  they  are  riveted  up 
complete  and  when  perfectly  aligned. 

161.  Field  Connections. — All  holes  for  field  rivets  in  splices  in  tension 
members  carrying  live  loads  shall  be  accurately  drilled  to  an  iron  tem- 
plet or  feamed  while  the  connecting  parts  are  temporarily  put  together. 

162.  Eye-Bars. — Eye-bars  shall  be  straight  and  true  to  size,  and 
shall  be  free  from  twists,  folds  in  the  neck  or  head,  or  any  other  defect. 
Heads  shall  be  made  by  upsetting,  rolling  or  forging.     Welding  will 
not  be  allowed.     The  form  of  heads  will  be  determined  by  the  dies  in 
use  at  the  works  where  the  eye-bars  are  made,  if  satisfactory  to  the 
engineer,  but  the  manufacturer  shall  guarantee  the  bars  to  break  in 
the  body  with  a  silky  fracture,  when  tested  to  rupture.     The  thickness 
of  head  and  neck  shall  not  vary  more  than  -£%  in.  from  the  thickness 
of  the  bar. 

163.  Boring  Eye-Bars. — Before  boring,  each  eye-bar  shall  be  prop- 
erly annealed  and  carefully  straightened.     Pin  holes  shall  be  in  the 
center  line  of  bars  and  in  the  center  of  heads.     Bars  of  the  same  length 


STEEL   FRAME   BUILDINGS.  4X9 

shall  be  bored  so  accurately  that,  when  placed  together,  pins  ^  in. 
smaller  in  diameter  than  the  pin  holes  can  be  passed  through  the  holes 
at  both  ends  of  the  bars  at  the  same  time. 

164.  Pin  Holes. — Pin  holes  shall  be  bored  true  to  gage,  smooth  and 
straight;  at  right  angles  to  the  axis  of  the  member  and  parallel  to  each 
other,  unless  otherwise  called  for.     Wherever  possible,  the  boring  shall 
be  done  after  the  member  is  riveted  up. 

165.  The  distance  center  to  center  of  pin  holes  shall  be  correct 
within  3*2  m->  and  the  diameter  of  the  hole  not  more  than  -gL  m.  larger 
than  that  of  the  pin,  for  pins  up  to  5  in.  diameter,  and  -fa  m-  f°r 
larger  pins. 

1 66.  Pins  and  Rollers. — Pins  and  rollers  shall  be  accurately  turned 
to  gage  and  shall  be  straight  and  smooth  and  entirely  free  from  flaws. 

167.  Pilot  Nuts. — At  least  one  pilot  and  one  driving  nut  shall  be 
furnished  for  each  size  of  pin  for  each  structure,  and  field  rivets  10 
per  cent  in  excess  of  the  number  of  each  size  actually  required. 

1 68.  Screw  Threads. — Screw  threads  shall  make  tight  fits  in  the 
nuts  and  shall  be  U.  S.  standard,  except  above  the  diameter  of  if  in., 
when  they  shall  be  made  with  six  threads  per  in. 

169.  Annealing. — Steel,  except  in  minor  details,  which  has  been 
partially  heated  shall  be  properly  annealed. 

170.  Steel  Castings. — All  steel  castings  shall  be  annealed. 

171.  Welds. — Welds  in  steel  will  not  be  allowed. 

172.  Bed  Plates. — Expansion  bed  plates  shall  be  planed  true  and 
smooth.     Cast  wall  plates  shall  be  planed  top  and  bottom.     The  cut  of 
the  planing  tool  shall  correspond  with  the  direction  of  expansion. 

173.  Shipping  Details. — Pins,  nuts,  bolts,  rivets,  and  other  small 
details  shall  be  boxed  or  crated. 

174.  Weight. — The  weight  of  every  piece  and  box  shall  be  marked 
on  it  in  plain  figures. 

175.  Finished  Weight. — Payment  for  pound  price  contracts  shall 
be  by  scale  weight.     Xo  allowance  over  2  per  cent  of  the  actual  total 
weight  of  the  structure  as  computed  from  the  shop  plans  will  be  allowed 
for  excess  weight. 


42O  SPECIFICATIONS. 

ADDITIONAL  SPECIFICATIONS  WHEN  GENERAL  REAMING  AND  PLANING 

ARE  REQUIRED. 

176.  Planing  Edges. — Sheared  edges  and  ends  shall  be  planed  off 
at  least  J  in. 

177.  Reaming. — Punched  holes  shall  be  made  with  a  punch  T3F  in. 
smaller  in  diameter  than  the  nominal  size  of  the  rivets  and  shall  be 
reamed  to  a  finished  diameter  of  not  more  than  TV  in.  larger  than 
the  rivet. 

178.  Reaming  after  Assembling. — Wherever  practicable,  reaming 
shall  be  done  after  the  pieces  forming  one  built  member  have  been 
assembled  and  firmly  bolted  together.     If  necessary  to  take  the  pieces 
apart  for  shipping  and  handling,  the  respective  pieces  reamed  together 
shall  be  so  marked  that  they  may  be  reassembled  in  the  same  position 
in  the  final  setting  up.     No  interchange  of  reamed  parts  will  be  allowed. 

179.  Removing  Burrs. — The  burrs  on  all  reamed  holes  shall  be 
removed  by  a  tool  countersinking  about  -fa  in. 

TIMBER. 

1 80.  Timber. — The  timber  shall  be  strictly  first-class  spruce,  white 
pine,  Douglas  fir,  Southern  yellow  pine,  or  white  oak  timber;  sawed 
true  and  out  of  wind,  full  size,  free  from  wind  shakes,  large  or  loose 
knots,  decayed  or  sapwood,  wormholes  or  other  defects  impairing  its 
strength  or  durability. 

PAINTING. 

181.  Painting. — All  steel  work  before  leaving  the  shop  shall  be 
thoroughly  cleaned  from  all  loose  scale  and  rust,  and  be  given  one 
good  coating  of  pure  boiled  linseed  oil  or  paint  as  specified,  well  worked 
into  all  joints  and  open  spaces. 

182.  In  riveted  work,  the  surfaces  coming  in  contact  shall  each  be 
painted  (with  paint)  before  being  riveted  together. 

183.  Pieces  and  parts  which  are  not  accessible  for  painting  after 
erection  shall  have  two  coats  of  paint. 

184.  The  paint  shall  be  a  good  quality  of  red  lead  or  graphite  paint, 
ground  with  pure  linseed  oil,  or  such  paint  as  may  be  specified  in  the 
contract. 

185.  After  the  structure  is  erected  the  iron  work  shall  be  thoroughly 
and  evenly  painted  with  two  additional  coats  of  paint,  mixed  with  pure 


STEEL    FRAME    BUILDINGS.  42 1 

linseed  oil,  of  such  quality  and  color  as  may  be  selected.  Painting  shall 
be  done  only  when  the  surface  of  the  metal  is  perfectly  dry.  No  paint- 
ing shall  be  done  in  wet  or  freezing  weather  unless  special  precautions 
are  taken.  The  two  field  coats  of  paint  shall  be  of  different  colors. 

1 86.  Machine  finished  surfaces  shall  be  coated  with  white  lead  and 
tallow  before  shipment  or  before  being  put  out  into  the  open  air. 

INSPECTION  AND  TESTING  AT  MILL  AND  THE  SHOPS. 

187.  The  manufacturer  shall  furnish  all  facilities  for  inspecting  and 
testing  weight  and  the  quality  of  workmanship  at  the  mill  or  shop 
where  material  is  fabricated.     He  shall  furnish  a  suitable  testing  ma- 
chine for  testing  full-sized  members  if  required. 

1 88.  Mill   Orders. — The   engineer   shall   be    furnished   with   com- 
plete copies  of  mill  orders,  and  no  materials  shall  be  ordered  nor  any 
work  done  before  he  has  been  notified  as  to  where  the  orders  have  been 
placed  so  that  he  may  arrange  for  the  inspection. 

189.  Shop  Plans. — The  engineer  shall  be  furnished  with  approved 
complete  shop  plans,  and  must  be  notified  well  in  advance  of  the  start 
of  the  work  in  the  shop  in  order  that  he  may  have  an  inspector  on 
hand  to  inspect  the  material  and  workmanship. 

190.  Shipping    Invoices. — Complete    copies    of   shipping   invoices 
shall  be  furnished  the  engineer  with  each  shipment. 

191.  The  engineer's  inspector  shall  have  full  access,  at  all  times, 
to  all  parts  of  the  mill  or  shop  where  material  under  his  inspection  is 
being  fabricated. 

192.  The  inspector  shall  stamp  each  piece  accepted  with  a  private 
mark.     Any  piece  not  so  marked  may  be  rejected  at  any  time,  and  at 
any  stage  of  the  work.     If  the  inspector,  through  an  oversight  or  other- 
wise, has  accepted  material  or  work  which  is  defective  or  contrary  to 
the  specifications,  this  material,  no  matter  in  what  stage  of  completion, 
may  be  rejected  by  the  engineer. 

193.  Full  Size  Tests. — Full  size  tests  of  any  finished  member  shall 
be  tested  at  the  manufacturer's  expense,  and  shall  be  paid  for  by  the 
purchaser  at  the  contract  price  less  the  scrap  value,  if  the  tests  are  sat- 
isfactory.    If  the  tests  are  not  satisfactory  the  material  will  not  be 
paid  for  and  the  members  represented  by  the  tested  member  may  be 
rejected. 


SPECIFICATIONS. 

ERECTION. 

194.  Tools. — The  contractor  shall  furnish  at  his  own  expense  all 
necessary  tools,  staging  and  material  of  every  description  required  for 
the  erection  of  the  work,  and  shall  remove  the  same  when  the  work  is 
completed. 

195.  Risks. — The  contractor  shall  assume  all  risks  from  storms  or 
accidents,  unless  caused  by  the  negligence  of  the  owner,  and  all  damage 
to  adjoining  property  and  to  persons  until  the  work  is  completed  and 
accepted. 

196.  The  contractor  shall  comply  with  all  ordinances  or  regulations 
appertaining  to  the  work. 

197.  The  erection  shall  be  carried  forward  with  diligence  and  shall 
be  completed  promptly. 


APPENDIX  II. 

PROBLEMS  IN  GRAPHIC  STATICS  AND  THE  CALCULATION  OF  STRESSES. 

Introduction. — It  is  impossible  for  the  student  to  gain  a  working 
knowledge  of  graphic  statics  and  the  calculation  of  stresses  without 
solving  numerous  problems.  In  order  to  save  the  time  of  the  student 
and  the  instructor  the  problems  must  be  selected  with  care,  and  the 
data  put  in  working  form.  The  following  problems  have  been  given 
by  the  author,  in  connection  with  a  course  preliminary  to  bridge  analysis, 
and  are  presented  here  with  the  hope  that  they  may  prove  of  value  to 
both  students  and  instructors.  By  slightly  changing  the  quantities  and 
dimensions  the  data  for  new  problems  may  be  easily  obtained. 

Instructions.— (i)  Plate.— The  standard  plate  is  to  be  9"  X  10^", 
with  a  i"  border  on  the  left-hand  side,  and  a  y2"  border  on  the  top, 
bottom,  and  right-hand  side  of  the  plate.  The  plate  inside  the  border  is 
to  be  jl/2"  X  9l/2tf.  (2)  Co-ordinates. — Unless  stated  to  the  contrary, 
co-ordinates  given  in  the  data  will  refer  to  the  lower  left-hand  corner 

1500 

of  border  as  the  origin  of  co-ordinates.     In  denning  the  force,  P  — 

150° 

(5.0",  3.0"),  the  force  is  1500  Ibs.,  makes  150°  with  the  X-axis  (lies 
in  the  second  quadrant),  and  passes  through  a  point  5.0"  to  the  right, 
and  3.0"  above  the  lower  left-hand  corner  of  border.  (3)  Data. — 
Complete  data  shall  be  placed  on  each  problem  so  that  the  solution 
will  be  self  explanatory.  (4)  Scales. — The  scales  of  forces,  and  of 
frames  or  trusses  shall  be  given  as  i"=  (  )  Ibs.,  or  ft.;  and  by  a 
graphic  scale  as  well.  (5)  Name. — The  name  of  the  student  is  be 
placed  outside  the  border  in  the  lower  right-hand  corner.  (6)  Equa- 
tions.— All  equations  shall  be  given,  but  details  of  the  solution  may 
be  indicated.  (7)  References. — References  are  to  "  The  Design  of 
Steel  Mill  Buildings." 

Note. — It  should  be  noted  that  all  the  problems  have  been  re- 
duced so  that  all  dimensions  are  one-half  the  original  dimensions  given 
in  the  statements  of  the  problems. 


424  PROBLEMS 

PROBLEM  i.    RESULTANT  OF  CONCURRENT  FORCES. 
(a)  Problem.  —  Given  the  following  concurrent  forces  : 
_I900  ^  950  1700  p   750  2200 

^o0'  23o°'  33i5°;  240°  '  5i5o°' 

Forces  are  given  in  pounds.  Required  to  find  the  resultant,  R,  by 
means  of  a  force  diagram.  Check  by  calculating  R  by  the  algebraic 
method.  Give  all  equations.  Also  construct  check  force  polygon. 
Give  amount  and  direction  of  the  resultant.  Scale  for  force  polygon, 


(b)  Methods.  —  Start  P1  at  point  4",  3*^"   (x,  y,  using  lower 
left-hand  corner  of  the  border  as  the  origin  of  co-ordinates)  and  take 
the   forces  in  the  order,  P±,  P2,  P3,  P4,  P5.     Draw   check  polygon 

starting   at    the    same   point    and    drawing   the    forces    in    the    order 
p     p     p     p     p 

r  2>    r  4>    r  5>    r  3>    r  !• 

(c)  Results.  —  The  resultant  is  a  force  R  acting  through  the  point 
of  intersection  of  the  given  forces,  and  is  parallel  to  the  closing  line 
in  the  force  polygon.     It  will  be  seen  that  it  is  immaterial  in  what 
order  the  forces  are  taken  in  calculating  the  resultant,  R.    In  the  alge- 
braic  solution   the   summation   of  the   horizontal   components   of   the 
forces,  including  the  resultant,  R,  are  placed  equal  to  zero,  and  the 
summation   of  the  vertical   components   of  the   forces,   including  the 
resultant,  R,  are  placed  equal  to  zero.     Solving  these  equations  we 
have  the  value  of  R,  and  the  angle  6,  which  R  makes  with  the  X-axis. 

PROBLEM  la.     RESULTANT  OF  CONCURRENT  FORCES. 
(a)  Problem.  —  Given  the  following  concurrent  forces: 


1800,  p  loop.  pI7OC).  P  _Z5^L.  p  2IO° 

120°'  2     0°  '  3i0'  424o°'  5i50°' 


Forces  are  given  in  pounds.  Required  to  find  the  resultant,  R,  by 
means  of  a  force  diagram.  Check  by  calculating  R  by  the  algebraic 
method.  Give  all  equations.  Also  construct  check  force  polygon. 
Give  amount  and  direction  of  the  resultant.  Scale  for  force  polygon> 
Ibs. 


PROBLEMS 


425 


Graphic    Statics. 


Problem   I. 


I"- 400 

"\ 

Algebraic  Solution.  Check  Force  PolYqon 

1 900  COS  ieO°-»-950c05300-H700cos3l50  Force  Poly<3°n 

+  750CO5  240°* 2200 COS  150°=  Rc059  Results 

1900Sinl20°-«-950sin300-l700Sin3150  By  Graphics.  R  = 

*750SinE40°+e200sin  150°=R5in6  e  =  13\°6 

tan 0  =-1.135      6*\3\*2$'    By  Algebra. 


426  PROBLEMS 

PROBLEM  2.     RESULTANT  OF  NON-CONCURRENT  FORCES. 
(a)  Problem.  —  Given  the  following  non-concurrent  forces  : 


720  270 

(7-0",  6.3"),    P.~(o-S",  9-3"),    P>~  (7-0",  6.6"), 


2IO 

P4—  (0.8",  8.5"). 

Forces  are  given  in  pounds.  Find  resultant,  R,  by  means  of  force 
and  equilibrium  polygons.  Check  by  calculating  R  by  means  of  a  new 
force  polygon  and  a  new  equilibrium  polygon.  Also  check  as  described 
below.  Scale  for  force  polygon,  i"  =  100  Ibs. 

(b)  Methods.—  Start  force  polygon  at   (7.0",  i.o").     Take  pole 
at  (3.8",  o.o").    Start  equilibrium  polygon  at  (7.0",  6.3").    Take  new 
pole  at  (2.2",  o.o"),  and  draw  new  polygon  starting  at  (7.0'',  6.3"). 

(c)  Results.  —  The  resultant  is  a  force,  R,  and  acts  through  the 
intersection  of  the  strings  d,  e  and  d'  ,  e'  ,  and  is  parallel  to  the  closing 
line  in  force  polygon.     If  corresponding  strings  in  equilibrium  polygon 
are  produced  to  an  intersection,  the  points  of  intersection,  i,  2,  3,  4,  5, 
will  lie  in  a  straight  line  which  will  be  parallel  to  the  line  O-O'  joining 
the  poles  of  the  force  polygons.     This  relation  is  due  to  the  reciprocal 
nature  of  the  force  and  equilibrium  polygons,  and  may  be  proved  as 
follows  :    In  the  force  polygon  the  force  P4  may  be  resolved  into  the 
rays  c  and  d,  it  may  likewise  be  resolved  into  the  rays  c'  and  d'.     In 
like  manner  it  may  be  seen  that  the  force  O-O'  can  be  resolved  into  the 
d  and  d',  or  into  c  and  c'.     Now  if  the  strings  d  and  d'  are  drawn 
through  the  point  4,  and  the  strings  c  and  c'  are  drawn,  they  must  in- 
tersect in  the  point  3,  and  4-3  must  be  parallel  to  O-O'.     For  the  re- 
sultant of  d  and  d'  is  equal  to  O-O'  and  must  act  in  a  line  parallel  to 
O-O';  likewise  the  resultant  of  c  and  c'  is  equal  to  O-O'  and  must 
act  parallel  to  O-O';  and  in  order  to  have  equilibrium  3-4  must  be 
parallel  to  O-O'. 

In  like  manner  it  may  be  proved  that  i,  2,  3,  4,  5,  are  in  a  straight 
line  parallel  to  O-O'. 

From  the  above  it  will  be  seen  that  to  have  equilibrium  in  a  sys- 
tem of  non-concurrent  forces  it  is  necessary  that  the  force  polygon  and 
its  corresponding  equilibrium  polygons  must  close,  or  that  two  equi- 
librium polygons  must  close. 


PROBLEMS 


427 


Equilibrium  R>\yqon 
Check  Equil.Polyqon 


PROBLEM  2a.     RESULTANT  OF  NON-CONCURRENT  FORCES. 
(a)  Problem. — Given  the  following  non-concurrent  forces : 

^  (7-o", 6.3"),    P^  (0.5", 9.3"),    P3 g^(7.o", 6.6"), 

P^(o.8",  8.5"). 

The  rest  of  the  statement  is  the  same  as  for  Problem  2. 
29 


428  PROBLEMS 

PROBLEM  3.    TEST  OF  EQUILIBRIUM  OF  FORCES. 
(a)  Problem.  —  Test  the  following  forces  for  equilibrium  by  means 
of  force  and  equilibrium  polygons  : 

7.8  10.8  12.2 

PI—  (475",  o.o")  ;    P2—  (4.75",  77")  ;    ^3—  (0.0",  7.0")  ; 


75",  6.4'');    P5          (275",  6.4'');    P6-(275",  77"). 


The  forces  are  given  in  tons.  Check  by  using  a  second  pole  and 
equilibrium  polygon;  also  draw  a  line  through  the  intersection  of  the 
corresponding  rays,  and  check  as  in  Problem  2.  Give  amount  and 
direction  of  the  equilibrant.  Scale  of  forces,  i"  =  5  tons. 

(b)  Methods.—  Start  force  polygon  at   (0.8",   1.5").     Take  first 
pole  at    (3.2",  2.7").     Start   equilibrium   polygon   at    (4.75",   9.1")  • 
Take  second  pole  at  (4.0",  3.2").    Start  second  equilibrium  polygon  at 
(475",  8.2"). 

(c)  Results.  —  If  the  system  of  forces  was  in  equilibrium  the  equi- 
librium polygons  would  close,  and  the  first  and  last  strings  /  and  /, 
and  /'  and  /'  would  coincide,  respectively.     The  equilibrant  will  be 
equal  to  a  couple  with  a  moment  represented  by  the  rays  /  or  /'  multi- 
plied by  the  distance  h  or  hr.    In  general  in  any  system  of  non-current 
forces  if  the  force  polygon  closes  the  equilibrant  of  the  system  is  a 
couple.    If  the  system  is  in  equilibrium  the  arm  of  the  couple  is  zero. 
It  is  evident  that  in  order  that  any  system  of  non-concurrent  forces 
be  in  equilibrium  it  is  necessary  that  both  the  force  polygon  and  an 
equilibrium  polygon  must  close.    The  check  line  must  be  parallel  to  the 
line  O-O'  joining  the  poles,  and  also  pass  through  the  intersections  of 
corresponding  rays  as  in  Problem  2. 

PROBLEM  3a.     TEST  OF  EQUILIBRIUM  OF  FORCES. 
(a)  Problem.  —  Test  the  following  forces  for  equilibrium  by  means 
of  force  and  equilibrium  polygons  : 


(475",  0.0")  ;    P2  (4.75",  7.7")  ;    Ps  (o.o",  7.0")  ; 


P4          (4.75",  6.4");    Pt          (2.75",  6.4"):    P(2.75",  7-7"). 


PROBLEMS 


429 


Graphic  5tatics. 


,--  .* * 

."        _*       I          a       -- 


Problem  3. 


^U75. 


7.1J 


p6 


i-'   --' 

-V,h,x-'  * 


«, 


S>^£OH^<  wN(  \ 

^(o,,o,       /^gS  |^.«>\\ 


tquilibrqnt-ACouple 
»f*h=»3.4*/e5-3:s5irv 

=  P6*h,=S.»>6» 
E.  by  check  cquil.  polygon 


The  forces  are  given  in  tons.  Check  by  using  a  second  pole  and 
equilibrium  polygon ;  also  draw  a  line  through  the  intersection  of  the 
corresponding  rays,  and  check  as  in  Problem  2.  Give  amount  and 
direction  of  the  equilibrant.  Scale  of  forces,  i"  =  5  tons. 


430  PROBLEMS 

PROBLEM  4.    RESOLUTION  OF  FORCES. 
(a)  Problem.  —  Given  the  following  forces: 


270  270  270 

Forces  are  given  in  tons,     (i)   Find  the  resultant,  R,  by  means  of 
force  and  equilibrium  polygons.     (2)  Resolve  R  into  two  parallel  forces 

?  ? 

P'  —  (3.2",  —  )  and  P"  -  -  (5.4",  —  )  .     (3)  Find  the  moment,  M,  of 
270°  90° 

R  about  a  point  Z  at  (4.0",  —  ).    Check  by  the  algebraic  method  giv- 
ing all  equations.    Scale  of  forces,  I  "  =  5  tons. 

(b)  Methods.—  Start   force   polygon   at    (5.7",   0.5"),   and   take 
pole  at  (1.7",  3.0").    In  the  algebraic  method  take  moments  about  the 
left  border  in  finding  the  point  of  application  of  R,  and  take  moments 
in  the  line  of  action  of  P"  in  resolving  R  into  P'  and  P". 

(c)  Results.  —  (i)  The  position  of  R  is  at  the  intersection  of 
strings  a  and  d.     (2)   Prolong  string  a  until  it  intersects  P',  take  the 
intersection  of  string  d  with  P"  ;  then  string  e  is  the  closing  line  of  the 
polygon.     (3)  The  moment  of  R  is  found  graphically  by  multiplying 
the  intercept,  y,  by  the  pole  distance,  H.     (4)   To  find  position  of  R 
algebraically  take  moment  of  Pa,  P2,  and  P3,  about  the  left  border,  and 
divide  by  R,  which  is  the  sum  of  Plf  P2,  P3.     (5)  The  moment  of  R 
about  Z  is  equal  to  R  X  (4.0  —  2.28)",  =  36.8  in.-tons. 

PROBLEM  43.     RESOLUTION  OF  FORCES. 
(a)  Problem.  —  Given  the  following  forces: 

I3-2  /"       \  .          5-°     f2Q"  _  "\  •     p  _4^_ 

~  (  3  270° 


Forces  are  given  in.  tons,     (i)   Find  the  resultant,  R,  by  means  of 
force  and  equilibrium  polygons.    (2)  Resolve  R  into  two  parallel  forces 

P'-^tf  (3-2",  —  )  and  P"  ^  (54",  —  )  •     (3)  Find  the  moment,  M,  of 

R  about  a  point  Z  at  (4.5",  —  )  .    Check  by  the  algebraic  method  giv- 
ing all  equations.     Scale  of  forces,  i"  —  5  tons. 


PROBLEMS 


431 


Graphic  Statics. 
•-«"- 


Problem  4. 


-3.2 

4, 


8\.A 
"X 


'"Ti'V'/''  ip"-9° 
/e 

y 

XI 


^ 


»0 


Scale  lrt=5Tons. 


Qrqphic  5oiution    ^^^ 
R»ei.4Tons.      m.s.s1.1 

P'-30.4T.  P"=9.0T. 


P, 


Center  of  moments  in  P." 

P*=3o.s-2i. 
.e  in.-Tons. 


432  PROBLEMS 

PROBLEM  5.    CENTER  OF  GRAVITY  OF  AN  AREA. 

(a)  Problem. — Find  the  center  of  gravity  of  the  given  figure 
about  the  X-  and  F-axes  by  graphics.     Give  the  co-ordinates  of  the 
C.  G.  referred  to  O  as  the  origin.    Show  all  force  and  equilibrium  poly- 
gons.   Check  by  the  algebraic  method  stating  all  equations.     Scale  of 
figure,  i"  =  i".    Scale  of  forces,  i"=  I  sq.  in. 

(b)  Methods.— Start  force  polygon  (b)  at  point  (2.9",  8.8")  and 
take  pole  at   (5.6",  54").     Start  force  polygon   (c)  at  (6.9",  0.6"), 
and  take  pole  at  (3.25",  2.8").     In  the  algebraic  check  take  moments 
about  the  left-hand  edge  and  the  lower  edge  of  the  figure. 

(c)  Results. — The  center  of  gravity  of  the  figure  will  come  at 
the  intersection  of  the  resultants  R  and  Rr,  which  is  at  the  center  of 
area.     The  areas  Plt  P2,  and  P3,  may  be  taken  as  acting  at  any 
angle,  but  maximum  accuracy  is  attained  when  the  forces  are  assumed 
as  acting  at  right  angles.     If  the  figure  has  an  axis  of  symmetry  (an 
axis  such  that  every  point  on  one  side  of  the  axis  has  a  corresponding 
point  on  the  other  side  at  the  same  distance  from  the  axis)  but  one  force 
and  equilibrium  polygon  is  required. 


PROBLEM  5a.    CENTER  OF  GRAVITY  OF  AN  AREA. 

(a)  Problem.— Find  the  center  of  gravity  of  a  6"  X  4"  X  i" 
angle  with  the  long  leg  vertical  and  short  leg  to  the  right  about  the 
X-  and  F-axes  by  graphics.  Give  the  co-ordinates  of  the  C.  G.  re- 
ferred to  O  as  the  origin.  Show  all  force  and  equilibrium  polygons. 
Check  by  the  algebraic  method  stating  all  equations.  Scale  of  figure, 
i"  =  2".  Scale  of  forces,  i"=2  sq.  in. 


PROBLEMS 


433 


6rophic  Statics. 


R       Problem  5. 


{.  —  -,  3/4--H\ 


(1.0.5.5) 


\    Pi 

^'<---K-f->-\- V 


?v~. 

I     xv 


I 

| >. 

Tc-6.- 


_?>_.  y\ 


Scale  Force  Di 


6rophjcj 


R1 


Alqebrg>ic  Check.  KXX^ 

A        ~  A  A-f>K  X^- 


4.485 


^5f; 

y  *  1.3 1 " 
C.6.-(.96J.3l") 


4.465 


434  PROBLEMS 

PROBLEM  6.    MOMENT  OF  INERTIA  OF  AN  AREA. 

(a)  Problem.     Calculate  the  moment  of  ineltia,  I,  of  a  standard 
9"  [@  13-25  Ibs.,  about  an  axis  through  its  center  at  right  angles  to 
the  web:    (i)    By  Culmann's  approximate  method;    (2)    by  Mohr's 
approximate  method;   (3)  by  the  algebraic  method.     Omit  the  fillets. 
Scale  of  channel,  i"  =  i" .    Scale  of  forces,  i"  =  I  sq.  in. 

(b)  Methods. — Divide  the  channel  into  convenient  sections  and 
consider  the  areas  as  forces  acting  through  their  centers  of  gravity.   ( I ) 
Culmann's  method  (Fig.  22).    Start  force  polygon  (a)  at  (3.5",  9.1")* 
and  take  pole  at  (5.45",  4-6").    Draw  equilibrium  polygon  (b).    Now 
with  intercepts  a-b,  b-c,  c-d,  d-e,  e-f,  f-g,  g-h,  h-i,  as  forces,  and  a 
new  pole  at    (4.5",  o.i")    construct  equilibrium  polygon    (d).     The 
moment  of  inertia  is  (approximately)  I  =  H  X  H'  X  y.     (2)  Mohr's 
method  (Fig.  23).    Calculate  the  area  of  the  equilibrium  polygon  (b) 
by  means  of  the  planimeter  or  by  dividing  it  into  triangles  and   (ap- 
proximately) /  =  area  equilibrium  polygon   (b)  X  2  H.       If  the  area 
is  divided  into  an  infinite  number  of  sections,  or  if  the  true  curve  of 
equilibrium  be  drawn  through  the  points  determined,  this  method  gives 
the  true  value  of  /.     (3)  Algebraic  method.     The  moment  of  inertia 
about  the  center  line  is  /  =  /'+  A  d2  +  2 1"    where  /'  =  moment  of 
inertia  of  the  main  rectangle ;  A  =  area  of  the  two  flanges ;  d  =  distance 
of  the  center  of  gravity  of  the  flanges  from  the  center  line ;  and  /"  = 
moment  of  inertia  of  each  flange  about  an  axis  through  its  center  of 
gravity  parallel  to  the  center  line. 

(c)  Results. — The  algebraic  method  gives  the  true  value  of  7; 
Mohr's  method  gives  a  value  more  nearly  correct  than  Culmann's 
method,  as  would  have  been  expected.     The  values  of  /  given  in  the 
various  hand-books  are  calculated  by  the  algebraic  method. 


PROBLEM  6a.    MOMENT  OF  INERTIA  OF  AN  AREA. 

(a)  Problem. — Calculate  the  moment  of  inertia,  7,  of  a  standard 
9"  [@  15  Ibs.,  about  an  axis  through  its  center  at  right  angles  to 
the  web:  (i)  By  Culmann's  approximate  method;  (2)  by  Mohr's 
approximate  method;  (3)  by  the  algebraic  method.  Omit  the  fillets. 
Scale  of  channel,  i"  =  i".  Scale  of  forces,  i"  =  i  sq.  in. 


PROBLEMS 


435 


Graphic  5tatics 


Problem   6. 


*— »i 


!       '.'.     V0>       \  '•  i      .'  '  / 

1 — -6A.__^  —  J.JL.L.     a.U 


Mohr's  Method. 
reQtqu;i.Po\y. 

5.234  »9. 47.1 


436  PROBLEMS 

PROBLEM  7.    CONSTRUCTION  OF  AN  INERTIA  ELLIPSE  AND  AN  INERTIA 

CIRCLE. 

(a)  Problem. — Given  the  following  data  for  an  angle  7"  X  3/4" 
X  i";  ^  =  9-50  sq.  in.,  71==7.53"4,  /2  =  45-37"*;  ^  =  0.89";  r2  = 
2.19";  rB  =  0.74" ;  tan  0  =  0.241;  C.  G.  (2.71",  0.96"),  see  Cambria, 
pp.   176,   177.      (i)   Construct  the  inertia  ellipse.      (2)   Construct  the 
inertia  circle.    Omit  the  fillets.    Scale  of  the  angle,  i"  =  i". 

(b)  Methods,     (i)  Inertia  Ellipse. — Construct  angle  a,  tan  a  = 
0.241 ;  and  draw  axes  3-3  and  4-4,  which  are  the  principal  axes  of  the 
inertia  ellipse.     Calculate  r4  from  the  relation  I^-{-  I2  =  Iz-\-  74,  from 
which  rx2  -f-  r22  =  r32  -f  r42,  and  r4  =32.25".     Construct  the  enclosing 
rectangle  of  the  ellipse  on  the  axes  3—3  and  4—4,  and  inscribe  an  ellipse 
in  this  rectangle ;  this  ellipse  is  the  central  inertia  ellipse. 

Calculate  Z^  from  the  relation  Z1-2  =  Al  X  /*i  X  &i  +  A2  X  h2 
X  k2.  Also  calculate  c±  and  c2  from  the  relation  Z1_2—Ac.Lr2  =  Ac2r.L. 
Compare  the  calculated  values  of  c^  and  c2  with  the  scaled  values  on  the 
ellipse.  -Note  that  c±  and  c2  are  zero  for  the  principal  axes. 

(  2  )  Inertia  Circle. — Calculate  the  product  of  inertia,  Zi_2  =  —  9.67. 
From  any  given  point,  a,  lay  off  7j  =  7.53  to  the  left  extending  to  b,  lay 
off  7.3  =  45.37  to  the  right  from  b,  and  extending  to  c.  At  a  erect  a 
perpendicular  a-d  =  Z-L_2  =  —  9.67.  Then  with  center  O,  midway 
between  a  and  c,  and  with  a  radius  O-d  describe  a  circle,  which  will 
be  the  inertia  circle.  A  line  drawn  through  d  and  e  will  be  parallel  to 
the  principal  axis  4-4,  and  the  diameter  of  the  inertia  circle  will  be 
the  maximum  value  of  72  —  71. 

(c)  Results. — (i)  The  inertia  ellipse  drawn  is  the  central  ellipse 
of  inertia,  and  is  the  smallest  ellipse  that  can  be  drawn.     The  radii  of 
gyration  about  any  axis  can  be  found  directly  from  the  inertia  ellipse. 
(2)  The  moments  of  inertia  about  any  axis  can  be  found  directly  from 
the  circle  of  inertia. 

PROBLEM  7a.     CONSTRUCTION  OF  AN  INERTIA  ELLIPSE  AND  AN  INERTIA 

CIRCLE. 

(a)  Problem.— Given  the  data  for  an  angle  7"X3>^"X%"; 
see  Cambria,  pp.  176,  177.  (i)  Construct  the  inertia  ellipse.  (2) 
Construct  the  inertia  circle.  Omit  the  fillets.  Scale  of  the  angle, 


PROBLEMS 


437 


Graphic  Statics. 


O.ZAI. 
Product  of  Inertia  ,Z  l-^  . 


Scale  of  Angle 
Nalural  5ize. 


References:  "The  Determination  of  Unit  Stresses  in  the  General  Case  of 
Flexure  "  by  Professor  L.  J.  Johnson  in  Assoc.  Eng.  Soc.,  Vol.  XXVIII ;  Ap- 
pendix D.  Maurer's  "  Technical  Mechanics " ;  Muller-Breslau's  "  Graphische 
Statik  der  Baukonstruktionen,"  Band  I. 


43 8  PROBLEMS 

PROBLEM  8.    STRESSES  IN  A  ROOF  TRUSS  BY  GRAPHIC  AND  ALGEBRAIC 

RESOLUTION. 

(a)  Problem. — Given  a  Fink  truss,  span  4o'-o",  pitch  30°  ;  trusses 
spaced  i2'-o" ;  load  40  Ibs.  per  sq.  ft.  of  horizontal  projection.    Calcu- 
late the  reactions  by  means  of  force  and  equilibrium  polygons.     Cal- 
culate the  stresses  by  graphic  resolution,  and  check  by  algebraic  resolu- 
tion.   Scale  of  truss,  i"  =  8'-o".    Scale  of  loads,  i"  =  6ooo  Ibs. 

(b)  Methods.— Start  force  polygon  at    (6.25",  5.6").     Lay  off 
the  loads  in  the  order  Plt  P2,  P\,  from  the  top  downward.     Construct 
a  force  polygon,  and  draw  an  equilibrium  polygon  as  in  Fig.  14,  and 
calculate  the  reactions  R^  and  R2  by  means  of  the  closing  line  as  in 
Fig.  15.     Construct  stress  diagram  beginning  at  L0  and  analyzing  the 
joints  in  the  order,  L0,  Ult  Li}  U2,  etc.,  checking  at  L'0.    Arrows  acting 
toward  joints  in  the  truss  and  toward  the  ends  of  the  lines  in  the 
stress  diagram  indicate  compression,  while  arrows  acting  away  from 
the  joints  and  ends  of  lines  respectively,  indicate  tension.     Use  one 
arrow  in  the  stress  diagram  the  first  time  a  force  is  used,  and  two 
arrows  the  second  time.     In  algebraic  resolution  the  sum  of  the  hori- 
zontal components  at  any  joint  are  placed, equal  to  zero,  and  the  sum 
of  the  vertical  components  are  placed  equal  to  zero,  and  the  solution 
of  these  two  sets  of  equations  gives  the  required  stresses. 

(c)  Results. — The  top  chord  is  in  compression,  while  the  bottom 
chord  is  in  tension.    In  the  Fink  truss  it  will  be  seen  that  the  long  web 
members  are  in  tension,  while  the  short  web  members  are  in  com- 
pression.   This  makes  the  truss  a  very  economical  one. 

PROBLEM  8a.     STRESSES  IN  A  ROOF  TRUSS  BY  GRAPHIC  AND  ALGEBRAIC 

RESOLUTION. 

(a)  Problem.— Given  a  Fink  truss,  span  4o'-o",  pitch  yz  ;  trusses 
spaced  ij-o" ;  load  40  Ibs.  per  sq.  ft.  of  horizontal  projection.  Calcu- 
late the  reactions  by  means  of  force  and  equilibrium  polygons.  Cal- 
culate the  stresses  by  graphic  resolution,  and  check  by  algebraic  resolu- 
tion. Scale  of  truss,  i"  =  8'-o".  Scale  of  loads,  i"  =  5ooo  Ibs. 


PROBLEMS 


439 


Graphic  Statics 


Scale  of  Truss   I'^e^ 
Scale  of  Stress  Dioqram^ 

l"=6ooo? 

Span  4O1o".  Trusses  i£-o"apart^ 

Load =4o*per  sq.fi.  ^-'"V1 

horizontal  proj.  ^''J~~_-;~~! 


sooo*     »zooo*^?X-c- 


Alqebro'\c  Resolution.  ^^       ^ 

•-•  FT*  -  12470*  •*•  \-X=  -^  14400*  J  L° 


4800-v  S- 

2  =  4160  * 


Graphic.  hX=  -n44oo,2-X=+l^ooo,^Y=-|^46ot3•Y=-e^oo,^t=^-3=4^oo? 


44°  PROBLEMS 

PROBLEM  9.    DEAD  LOAD  STRESSES  IN  A  TRIANGULAR  TRUSS  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o" ;  pitch  y$  \ 
camber  of  the  bottom  chord  3'-o" ;  trusses  spaced  i4'-o" ;  load  40  Ibs. 
per  sq.  ft.  of  horizontal  projection.     Calculate  the  reactions  by  means 
of  force  and  equilibrium  polygons.     Calculate  the  stresses  by  graphic 
resolution.    Scale  of  truss,  i"  =  lo'-o".    Scale  of  loads,  i"  =  5000  Ibs. 

(b)  Methods.— Start  the  truss  at  (0.75",  7.0").    Start  the  stress 
diagram  at    (6.75",  6.25").     Calculate  the  stresses  beginning  at  Rlf 
as  described  in  Fig.  27,  using  care  to  analyze  each  joint  before  pro- 
ceeding to  the  next.    Check  at  R2. 

(c)  Results. — The  upper  chord  is  in  compression  while  the  lower 
chord  is  in  tension.    The  vertical  web  members  are  in  compression  while 
the  inclined  web  members  are  in  tension  for  dead  loads.     As  a  check 
the  points  2,  4,  6,  should  be  in  a  straight  line.    The  partial  loads  coming 
on  the  reactions  (not  shown)  are  not  considered  as  they  have  no  effect 
on  the  stresses  in  the  truss.     This  truss  is  a  triangular  Pratt  and  is 
quite  economical,   but   is   somewhat  more   expensive  in   material   and 
labor  than  the  Fink  truss.     This  type  of  truss  is  much  used  for  com- 
bination trusses,  in  which  the  tension  members  are  made  of  iron  or 
steel,  while  the  compression  members  are  made  of  timber.     The  dead 
joint  load  will  be  equal  to  the  horizontal  projection  of  the  area  sup- 
ported by  a  panel  point,  multiplied  by  the  dead  load  per  square  foot, 
is  equal  to  14  X  7i  X  40  =  4200  Ibs. 


PROBLEM  9a.     DEAD   LOAD   STRESSES   IN   A  TRIANGULAR  TRUSS   BY 

GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o" ;  pitch  y3  ; 
camber  of  the  bottom  chord  2'-o";  trusses  spaced  i6'-o";  load  40  Ibs. 
per  sq.  ft.  of  horizontal  projection.  Calculate  the  reactions  by  means 
of  force  and  equilibrium  polygons.  Calculate  the  stresses  by  graphic 
resolution.  Scale  of  truss,  i"  =  lo'-o".  Scale  of  loads,  i"  =  5000  Ibs. 


PROBLEMS 


441 


ft          Problem  9. 

9         \y  _•_._» 


O'         S"        K> 


5colc  T«  U3-d 

p; 


Pratt  Trus 
Dead  Loads. 

Trusses  spaced  \4-ollc.toc, 
Load  =4o*per  sc^.ft.  hor.  proj 


442  PROBLEMS 

PROBLEM  10.     WIND  LOAD  STRESSES  IN  A  TRIANGULAR  TRUSS — No 
ROLLERS — BY   GRAPHIC   RESOLUTION. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o",  pitch  y3, 
camber  of  lower  chord  3'-o",  trusses  spaced  i4'-o",  wind  load  normal 
component  of  a  horizontal  wind  load  of  30  Ibs.  per  sq.  ft.,  no  rollers. 
Calculate  the  reactions  by  means  of  force  and  equilibrium  polygons. 
Calculate  the  stresses  by  graphic  resolution.    Take  P  as  3300  Ibs.    Scale 
of  truss,  i"=io'-o".    Scale  of  loads,  i"  =  3ooo  Ibs. 

(b)  Methods.— Start  stress  diagram  at  (4.65",  6.6").    The  reac- 
tions will  be  parallel  to  each  other  and  to  the  resultant  of  the  external 
loads.     The  equilibrium   polygon   may  be   started   at  any  convenient 
point  in  one  reaction,  closing  up  on  the  other  one.     The  closing  line 
of  the  equilibrium  polygon  will  always  have  its  end  in  the  reactions. 
The  calculation  of  stresses  is  begun  at  R±,  and  is  checked  up  at  R2. 

(c)  Results. — The  stresses  are  of  the  same  kind  in  the  chords 
as  for  dead  loads  as  given  in  Problem  9,  while  the  webs  on  the  leeward 
side  are  not  stressed.    The  load  P0  has  no  effect  on  the  stresses  in  the 
truss.    Calculate  the  vertical  component  of  the  wind  load  by  means  of 
Duchemin's  formula  (5),  as  plotted  in  Fig.  6  (page  15).    The  normal 
wind  joint  load  will  be  equal  to  14  X  9  X  26  =  3276,  which  is  taken 
as  3300  Ibs.     For  a  discussion  on  the  different  conditions  of  the  ends 
of  trusses,  see  Chapter  VII. 


PROBLEM  loa.    WIND  LOAD  STRESSES  IN  A  TRIANGULAR  TRUSS — No 

ROLLERS — BY  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o",  pitch  J^, 
camber  of  lower  chord  2'-o",  trusses  spaced  i6'-o",  wind  load  normal 
component  of  a  horizontal  wind  load  of  30  Ibs.  per  sq.  ft.,  no  rollers. 
Calculate  the  reactions  by  means  of  force  and  equilibrium  polygons. 
Calculate  the  stresses  by  graphic  resolution.  Take  P  as  3800  Ibs. 
Scale  of  truss,  i"  =  lo'-o".  Scale  of  loads,  i"  =  3000  Ibs. 


PROBLEMS 


443 


Graph 


Scale 


Problem  10. 


Pro-H  Trus; 
Wind  Load 
No  Rollers. 


Horizontal  Wind  Load. 

3o*per.  sq.ft. 
Normal  Comp.  •=  Z6**p.  sq.ft. 


Trusses  spaced  i4-o"c.toc.        (from  Diagram,  Fiq. 6, 

for  Duchemin's  FormulaV 


444  PROBLEMS 

PROBLEM  n.    DEAD  LOAD  STRESSES  IN  A  FINK  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Fink  truss,  span  6o'-o",  pitch  */$,  camber 
of  lower  truss  3'-o",  trusses  spaced  H'-O",  load  40  Ibs.  per  sq.  ft.  of 
horizontal  projection.     Calculate  the  reactions  by  means  of  force  and 
equilibrium   polygons.     Calculate  the   stresses  by  graphic   resolution. 
Scale  of  truss,  i"  =  lo'-o".    Scale  of  loads,  i"  =  5000  Ibs. 

(b)  Methods.— Start  the  truss  at  (0.75",  7.0").     Start  the  stress 
diagram  at    (6.75",   6.25").     Calculate  the  stresses  as  described  in 
Figs.  30  and  34,  replacing  the  members  4-5  and  5-6,  temporarily  by  the 
dotted  member  shown.     The  stress  diagram  is  then  carried  through 
to  the  point  7,  and  then  the  stresses  in  members  5-6  and  4-5  are  easily 
obtained.    Carry  the  stress  diagram  through  and  check  at  R2. 

(c)  Results. — The  upper  chord  is  in  compression  and  the  lower 
chord  is  in  tension,  the  stresses  being  practically  the  same  as  in  the 
triangular  truss  in  Problem  9.     In  the  webs  it  will  be  seen  that  the 
long  members  are  in  tension,  while  the  short  members  are  in  com- 
pression.   The  loads  coming  on  the  reaction  are  not  considered,  as  they 
have  no  effect  on  the  stresses  in  the  truss,  as  can  be  seen  by  comparing 
with  the  truss  in  Fig.  30.     As  a  check  the  points  i,  2,  5,  6,  in  the 
stress  diagram  should  be  in  a  straight  line.    The  dead  joint  load  will  be 
equal  to  the  horizontal  projection  of  the  area  supported  by  a  panel 
point,  multiplied  by  the  dead  load  per  square  foot,  is  equal  to  14  X7//2 
X  40  =  4200  Ibs. 


PROBLEM  na.    DEAD  LOAD  STRESSES  IN  A  FINK  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Fink  truss,  span  6o'-o",  pitch  y$,  camber 
of  lower  truss  2'-o",  trusses  spaced  i6'-o",  load  40  Ibs.  per  sq.  ft.  of 
horizontal  projection.  Calculate  the  reactions  by  means  of  force  and 
equilibrium  polygons.  Calculate  the  stresses  by  graphic  resolution. 
Scale  of  truss,  i"  =  lo'-o".  Scale  of  loads,  1^  =  5000  Ibs. 


PROBLEMS 


445 


Graphic  5-Va-Vics.    *o 


10 


FinKTru&s. 
Dead  Loads. 


446  PROBLEMS 

PROBLEM  12.    WIND  LOAD  STRESSES  IN  A  FINK  TRUSS — ROLLERS  LEE- 
WARD— BY  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  same  truss  as  in  Problem  n.     Wind 
load  to  be  the  normal  component  of  a  horizontal  wind  load  of  30  Ibs.  per 
sq.  ft.    The  truss  is  assumed  to  have  frictionless  rollers  under  the  lee- 
ward side.    Calculate  the  reactions  by  means  of  force  and  equilibrium 
polygons.    Calculate  the  stresses  by  graphic  resolution.    Scale  of  truss, 
i"  =  IQ'-O".    Scale  of  loads,  i"  =  3000  Ibs. 

(b)  Methods.— Start    stress    diagram    at    (4.75",  6.55").     The 
reaction   R2   will   be   vertical,   while   the   direction   of   R±   will   be 
unknown.     Use  the  method  of  calculating  the  reactions  described  on 
page  51,  and  in  Fig.  33;  noting  that  the  vertical  components  of  the 
reactions  are  independent  of  the  conditions  of  the  ends  of  the  truss. 
In  calculating  the  stresses  the  ambiguity  of  stresses  at  point  3-4-7-4-3; 
is  removed  by  substituting  the  dotted  member  shown,   for  members 
4-5  and  5-6.     The  calculation  of  the  stresses  is  begun  at  Rlt  and  is 
checked  up  at  R2. 

(c)  Results. — The  load  P1  has  no  effect  on  the  stresses  in  the 
truss.    The  stresses  in  the  members  are  of  the  same  kind  as  for  dead 
loads  as  given  in  Problem  n,  except  that  there  are  no  stresses  in  the 
web  members  on  the  leeward  side. 


PROBLEM  I2a.    WIND  LOAD  STRESSES  IN  A  FINK  TRUSS — ROLLERS 
LEEWARD — BY  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  same  truss  as  in  Problem  na.  Wind 
load  to  be  the  normal  component  of  a  horizontal  wind  load  of  30  Ibs. 
per  sq.  ft.  The  truss  is  assumed  to  have  frictionless  rollers  under  the 
leeward  side.  Calculate  the  reactions  by  means  of  force  and  equili- 
brium polygons.  Calculate  the  stresses  by  graphic  resolution.  Scale 
of  truss,  i"  =  lo'-o".  Scale  of  loads,  i"  =  3000  Ibs. 


PROBLEMS 


447 


Graphic  <5tat\cs. 
o'     s1     10'     * 


Problem  12. 

Same  truss  as 
in  Prob\em\\. 
RoUers  Leeward 


Scale  f= 


3000 


Horizontal  Wind  Load 
*  30*  per*  sq.ft. 
'Normal  Comp.=26*p.saft. 


(approx.) 


448  PROBLEMS 

PROBLEM  13.    WIND  LOAD  STRESSES  IN  A  FINK  TRUSS — ROLLERS  ON 
THE   WINDWARD   SIDE — BY   GRAPHIC   RESOLUTION. 

(a)  Problem. — Given  the  same  truss  and  wind  load  as  in  Prob- 
lem 12,  and  with  rollers  under  the  windward  side.    Calculate  the  reac- 
tions  by   means   of   force   and   equilibrium   polygons.      Calculate   the 
stresses  by  graphic  resolution.     Scale  of  truss,  i"  =  lo'-o".    Scale  of 
loads,  i  "  =  3000  Ibs. 

(b)  Methods. — Start  stress  diagram  at    (4.6",  6.7").     Reaction 
R!  will  be  vertical,  while  the  direction  of  R2  will  be  unknown,  the  only  • 
known  point  in  its  line  of  action  being  at  the  right  end  of  the  truss. 
Use  the  method  for  finding  the  reactions  described  on  page  52  and  in 
Fig.  34.     In  this  solution  the  equilibrium  polygon  is  started  at  the 
right  reaction,  the  only  known  point  in  R2,  and  the  polygon  is  drawn. 
The  intersection  of  ^  in  the  force  polygon,  and  a  line  through  0, 
parallel  to  the  closing  line  is  at  Yt  and  R2  is  then  determined  in  magni- 
tude and  direction.    The  stress  diagram  is  carried  through  and  checked 
at  R2. 

(c)  Results. — The  load  P1  must  be  considered  as  it  produces 
stresses  in  the  truss.     If  R2  coincides  with  the  top  chord  there  will 
be  no  stresses  in  the  other  members  of  the  truss  on  the  leeward  side; 
if  line  of  action  of  R2  passes  outside  and  above  the  truss  the  lower 
chord  will  be  in  tension ;  while  if  the  line  of  action  is  below  the  upper 
chord  the  lower  chord  will  be  in  compression.     These  statements  may 
be  checked  by  taking  moments  about  the  upper  peak  of  the  truss.     It 
will  be  seen  in  Problems  n,  12,  and  13  that  there  will  be  no  reversal 
of  stress  when  the  dead  load  and  wind  load  stresses  are  combined. 
This  is  commonly  true  for  simple  Fink  trusses  resting  on  walls;  but 
is  not  true  for  Fink  trusses  supported  on  columns,  nor  is  it  always 
true  for  Fink  trusses  simply  supported. 

PROBLEM  I3a.    WIND  LOAD  STRESSES  IN  A  FINK  TRUSS — ROLLERS  ON 

THE  WINDWARD  SIDE — BY  GRAPHIC  RESOLUTION. 
(a)  Problem. — Given  the  same  truss  and  wind  load  as  in  Prob- 
lem I2a,  and  with  rollers  under  the  windward  side.  Calculate  the  reac- 
tions by  means  of  force  and  equilibrium  polygons.  Calculate  the 
stresses  by  graphic  resolution.  Scale  of  truss,  i"  =  lo'-o".  Scale  of 
loads,  i "  =  3000  Ibs. 


PROBLEMS 


449 


Graphic  5tat»c5 


Problem  13. 

Some  truss  as 
in  Problem  II. 
Rollers  windwcm 


Scale  i" 


Horizontal  Wind  Load 

50* per  sc\.ft. 
Norma\  Component 

p.  ,*xiflS*2Sxz6-3300* 


45°  PROBLEMS 

PROBLEM  14.     WIND  AND  CEILING  LOAD  STRESSES  IN  AN  UNSYM- 
METRICAL  TRUSS,  BY  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  unsymmetrical  triangular  truss,  span 
5o'-o",   height    i6'-o",    rollers   leeward,   wind   joint   load   4000   Ibs., 
ceiling  joint  load  3000  Ibs.     Calculate  the  stresses  due  to  both  systems 
of  loading  by  graphic  resolution.     Scale  of  truss,  i"  =  8'-o".     Scale 
of  loads,  i"  =  4000  Ibs. 

(b)  Methods. — Calculate  the   reactions   due  to  the  wind  loads, 
using  the  method  of  Fig.  33.     Calculate  the  reactions  due  to  ceiling 
loads.    Then  place  the  y  point  of  the  wind  load  line  on  the  point  separat- 
ing the  ceiling  load  reactions  (the  x  point).    The  wind  loads  are  laid  off 
in  order  downwards,  while  the  ceiling  loads  are  laid  off  in  order  upwards. 
The  left  reaction,  Rlt  is  the  resultant  of  Rlw  and  R1T>  while  the  right  reac- 
tion, ^2,  is  the  resultant  of  R2W  and  R^.     The  calculation  of  the 
stresses  is  begun  at  Rlf  as  in  Problem   10.     The  stresses  are  then 
calculated  by  passing  to  joint  Clt  then  to  joint  P2,  then  to  C2,  etc.,  until 
the  stress  diagram  is  checked  up  at  R2. 

(c)  Results. — The  members  1-2  and  7-8  are  simply  hangers  to 
carry  the  ceiling  loads.    The  triangular  truss  in  this  problem  is  of  the 
Howe  type,  the  verticals  being  in  tension,  while  the  diagonal  web  mem- 
bers are  in  compression.     This  truss  is  expensive  to  build  of  iron  or 
steel  but  is  quite  a  satisfactory  type  where  iron  is  expensive  and  wood 
is  cheap,  and  is  used  for  the  struts. 


PROBLEM  i4a.    WIND  AND  CEILING  LOAD  STRESSES  IN  AN  UNSYM- 
METRICAL TRUSS,  BY  GRAPHIC  RESOLUTION. 
(a)  Problem. — Given  the   unsymmetrical  triangular  truss   span 
5o'-o",  height,  i6'-o",  rollers    windward,  wind  joint  load  4000  Ibs., 
ceiling  joint  load  3000  Ibs.    Calculate  the  stresses  due  to  both  systems 
of  loading  by  graphic  resolution.     Scale  of  truss,  i"  =  8'-o".     Scale 
of  loads,  i  "  =  4000  Ibs. 


PROBLEMS 


Graphic  Staff cs. 


Problem  \4. 


-tf-b*  ~«i-    o-o"-  -*    -  -  io-ou-     -  - 


HoUers  Leeward. 


452  PROBLEMS 

PROBLEM    15.     DEAD  LOAD   STRESSES  IN   A  TRIANGULAR  TRUSS  BY 
GRAPHIC  AND  ALGEBRAIC  MOMENTS. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o",  pitch  J4» 
trusses  spaced  i5'-o",  dead  load  40  Ibs.  per  sq.  ft.  of  horizontal  pro- 
jection.    Calculate  the  stresses  by  graphic  moments.     Check  by  calcu- 
lating the  stresses  by  algebraic  moments,  giving  all  equations.     Scale 
of  truss,  i"  =  io'-o".    Scale  of  loads,  i"  =  10,000  Ibs.    Use  pole  dis- 
tance H  =  30,000  Ibs. 

(b)  Methods. — Use  the  methods  for  algebraic  and  graphic  mo- 
ments described  in  Fig.  28  and  Fig.  29,  respectively.     Calculate  all 
moment  arms  and  check  by  scaling  from  the  diagram.     The  pole  dis- 
tance is  measured  in  pounds,  while  the  intercepts  are  measured  to  the 
same  scale  as  the  truss.    Take  the  section  and  choose  the  center  of  mo- 
ments so  that  but  one  unknown  force  will  produce  moments.     Take 
the  unknown  external  force  as  acting  from  the  outside  toward  the 
cut  section,  the  sign  of  the  result  if  plus  will  indicate  compression, 
if  minus  tension.     Be  careful  to  take  forces  on  one  side  of  the  cut 
section  only. 

(c)  Results. — The  kinds  of  stress  in  the  members  are  the  same  as 
in  Problem  9.    The  center  of  moments  used  in  calculating  each  stress 
can  be  easily  determined  from  the  equations.     The  method  of  alge- 
braic moments  is  much  used  for  calculating  stresses  in  bridges,  and 
other  frameworks  which  carry  moving  loads.     The  method  of  graphic 
moments  is  used  principally  as  an  explanatory  method. 


PROBLEM   I5a.    DEAD  LOAD  STRESSES  IN  A  TRIANGULAR  TRUSS  BY 

GRAPHIC  AND  ALGEBRAIC  MOMENTS. 

(a)  Problem. — Given  a  triangular  truss,  span  6o'-o",  pitch  J^, 
trusses  spaced  i6'-o",  dead  lead  40  Ibs.  per  sq.  ft.  of  horizontal  pro- 
jection. Calculate  the  stresses  by  graphic  moments.  Check  by  calcu- 
lating the  stresses  by  algebraic  moments,  giving  all  equations.  Scale 
of  truss,  i"=  IQ'-O".  Scale  of  loads,  i"  —  10,000  Ibs.  Use  pole  dis- 
tance H  =  30,000  Ibs. 


PROBLEMS 


453 


Graphic  Statics. 


Problem   \5. 


'-o".    Pitch 


pun  =  eo-o.     riTcn-^  ;        ?'+-'"  ' 

Spacing  «i5-o"<^to  ^.  (>!>C^       £rz"-  "~vi 

Load inq=4o*persq.flhor.  pro].  ""C^-^^  -  --< 


454  PROBLEMS 

PROBLEM    16.     DEAD  LOAD  STRESSES  IN  A  CANTILEVER  TRUSS  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  Fink  cantilever  truss,  span  4o'-o",  depth 
i2'-o",  joint  load  2000  Ibs.    Calculate  the  reactions  by  means  of  force 
and  equilibrium  polygons.    Calculate  the  stresses  by  graphic  resolution. 
Scale  of  truss,  i"  =  8'-o".    Scale  of  loads,  i"  =  1500  Ibs. 

(b)  Methods. — Calculate  the  reactions  as  in  Fig.   16,  page  30, 
noting  that  the  loads  in  the  two  cases  are  laid  off  in  different  order. 
Note  that  the  two  reactions  and  the  resultant  of  the  external  loads  meet 
in  a  point,  and  that  the  reactions  can  be  determined  by  means  of  this 
principle.    The  stress  diagram  is  started  with  the  load  P±  and  is  closed 
at  R1  and  R2. 

(c)  Results. — The  upper  chord  is  in  tension,  while  the  bottom 
chord  is  in  compression,  which  is  the  reverse  of  conditions  in  simple 
trusses.    In  calculating  the  stresses  due  to  wind  load  in  this  truss,  the 
reaction  R1  will  be  in  the  line  of  7-4,  and  R2  will  pass  through  A,  as 
in  the  case  of  dead  loads.    The  resultant  of  the  wind  loads  and  the  two 
reactions  will  meet  in  a  point,  and  the  solution  is  essentially  the  same 
as  for  dead  loads.     It  should  be  noted  that  the  closing  line  of  the 
equilibrium  polygon,  A-a,  has  its  ends  on  the  line  of  action  of  the 
resultants  R±  and  R2. 


PROBLEM    i6a.     DEAD  LOAD   STRESSES  IN  A  CANTILEVER  TRUSS  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  Fink  cantilever  truss,  span  5p'-o",  depth 
i5'-o",  joint  load  2500  Ibs.  Calculate  the  reactions  by  means  of  force 
and  equilibrium  polygons.  Calculate  the  stresses  by  graphic  resolution. 
Scale  of  truss,  i"  =  8'-o".  Scale  of  loads,  i"  =  20OO  Ibs. 


PROBLEMS 


455 


Oraphic  Statics. 


XA      Problem!  6. 


eooo* 


O*        1500*     3000*    Tru&s5cale  T-e'-o1 


Load  5 ca  I e  i"- 1 soo . 


45  6  PROBLEMS 

PROBLEM  17.    CALCULATION  OF  THE  DEFLECTION  OF  A  STEEL  BEAM  BY 

GRAPHICS. 

(a)  Problem. — Given  a  12"  I  @  31^2'  Ibs.  per  foot,  span  4o'-o", 
load  5000  Ibs.  applied  i6'-o"  from  the  left  support.     7  =  215.8  in.4. 
E  =  28,000,000.    Calculate  the  maximum  deflection  due  to  the  load,  and 
the  maximum  deflection  under  the  load  by  the  graphic  method.    Scale  of 
beam,    i"  =  6'-o".     Scale  of   loads,    i"  — 2000  Ibs.     Pole   distance, 
H  =  4.000  Ibs.    Scale  of  areas,  i"  =  60  sq.  ft.    Pole  distance,  H'  =  240 
sq.  ft. 

(b)  Methods. — Construct  force  polygon   (a)  and  draw  bending- 
moment  polygon  (b).    Divide  polygon  (b)  into  segments,  and  assume 
that  each  area  acts  as  a  load  through  its  center  of  gravity.     Construct 
force  polygon  (c),  and  draw  equilibrium  polygon   (d).     Polygon   (d) 
is  a  curve  which  has  ordinates  proportional  to  the  true  deflections. 

(c)  Results. — The  maximum  deflection  comes  between  the  load 
and  the  center  of  the  beam.    If  the  area  of  the  polygon  (b)  was  meas- 
ured in  square  inches  and  the  ordinates  in  (d)  measured  in  inches  the 
deflection  would  be  A  =  y  X  H  X  H'  -f-  E  I.    In  the  problem  this  result 
must  be  multiplied  by  1728.     The  closing  lines  of  polygons   (b)  and 
(d)  need  not  be  horizontal.     The  solution  given  above  may  be  very 
simply  stated  as  follows :  Construct  the  bending-moment  polygon  for 
the  given  loading  on  the  beam.     Load  the  beam  with  this  bending- 
moment  polygon,  and  with  a  force  polygon  having  a  pole  distance  equal 
to  E  I,  construct  an  equilibrium  polygon ;  this  polygon  will  be  the  elastic 
curve  of  the  beam.     It  is  not  commonly  convenient  to  use  a  pole  dis- 
tance equal  to  E  I,  and  a  pole  distance  H  is  used,  where  n  H  equals  E  I. 
For  a  discussion  of  this  subject  see  Chapter  XVa. 


PROBLEM  173.    CALCULATION  OF  THE  DEFLECTION  OF  A  STEEL  BEAM 

BY  GRAPHICS. 

(a)  Problem. — Given  a  12"  I  @  31^2  Ibs.  per  foot  span  4o'-o", 
load  3000  Ibs.  applied  i6'-o"  from  the  left  support,  and  3000  Ibs. 
applied  i2'-o"  from  the  right  support.  7  =  215.8  in.4.  £  =  28,000,- 
ooo.  Calculate  the  maximum  deflection  due  to  the  load,  and  the 
maximum  deflection  under  the  load  by  the  graphic  method.  Scale  of 


PROBLEMS 


457 


Graphic  Statics 


Scale  i"« 60  sq.ft. 

i    «*     °,' 
A.    V'XHx"1 


2  B, OOO,OOO*  El 5.8 

A  under  load 


28,000,000  XS15.8 


1.77. 


beam,  i"  =  6'-o".  Scale  of  loads,  i"  =  2OOO  Ibs.  Pole  distance, 
H  =  4000  Ibs.  Scale  of  areas,  i"  =  60  sq.  ft.  Pole  distance,  //'  =  240 
sq.  ft. 


458  PROBLEMS 

PROBLEM  18.    DEAD  LOAD  STRESSES  IN  A  WARREN  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Warren  truss,  span  I2o'-o",  panel  length 
2o'-o",  depth  2o'-o",  dead  load  700  Ibs.  per  ft.  per  truss.     Calculate 
the  dead  load  stresses  by  graphic  resolution.    Scale  of  truss,  i"-i6'-o". 
Scale  of  loads,  i"  =  12,000  Ibs. 

(b)  Methods. — The  loads  beginning  with  the  first  load  on  the 
left  are  laid  off  from  the  bottom  upwards.     The  calculation  of  the 
stresses  is  started  at  the  left  reaction,  and  the  stress  diagram  is  closed 
at  the  right  reaction.     For  additional  information  on  the  solution  see 
page  70. 

(c)  Results. — The  top  chord  is  in  compression,  the  bottom  chord 
is  in  tension;  all  web  members  leaning  toward  the  center  of  the  truss 
are  in  compression,  while  the  web  members  leaning  toward  the  abut- 
ments are  in  tension.    All  web  members  meeting  on  the  unloaded  chord 
(top  chord)  have  stresses  equal  in  amount  but  opposite  in  sign.    The 
stresses  in  the  lower  chord  are  the  arithmetical  means  of  the  stresses 
in  the  top  chord.    The  Warren  truss  is  commonly  made  of  iron  or  steel, 
the  most  common  section  for  the  members  being  two  angles  placed  back 
to  back. 


PROBLEM  i8a.    DEAD  LOAD  SRESSES  IN  A  WARREN  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Warren  truss,  span  i26'-o",  panel  length 
i8'-o",  depth  2o'-o",  dead  load  700  Ibs.  per  ft.  per  truss.  Calculate 
the  dead  load  stresses  by  graphic  resolution.  Scale  of  truss,  i"  — 
i5'-o".  Scale  of  loads,  i"  =  12,000  Ibs. 


PROBLEMS 


459 


Graphic  Statics.  Problem   IO 

j.  Warren  Truss.  ~ 

Graphic  Resolution 

*?5000  ^  _+  50000 +634-00^  „  +56OOO +35OOO . 


K 

r— -so-o-H     Y 

Dead  Load  7oo*per  linea\ 

foot  per  truss 
Equal  Joint  Loads,  f; 


Pane\  length, l,*2o-o 


Dead  Load  Stress  Diagram 


460  PROBLEMS 

PROBLEM  19.    DEAD  LOAD  STRESSES  IN  A  HOWE  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Howe  truss,  span  i6o'-o",  panel  length 
2o'-o",  depth  24'-o",  dead  load  600  Ibs.  per  lineal  foot  of  truss.    Calcu- 
late the  dead  load  stresses  by  graphic  resolution.     Scale  of  truss,  i"  = 
25'-o".    Scale  of  loads,  i"  =  15,000  Ibs. 

(b)  Methods. — The  loads  beginning  with  the  first  load  on  the  left 
are  laid  off  from  the  bottom  upwards.    Calculate  the  stresses  by  graphic 
resolution,  beginning  at  R^  and  checking  at  R2)  following  the  order 
shown  in  the  stress  diagram. 

(c)  Results. — The  top  chord  is  in  compression  and  the  bottom 
chord  is  in  tension  as  in  the  Warren  truss.    All  inclined  web  members 
are  in  compression,  while  all  vertical  web  members  are  in  tension.    The 
stresses  in  the  verticals  are  equal  to  the  vertical  components  of  the 
diagonal  members  meeting  them  on  the  unloaded  chord.     Stresses  in 
certain  panels  in  top  and  bottom  chords  are  equal. 

The  Howe  truss  is  commonly  built  with  timber  upper  and  lower 
chords  and  diagonal  struts,  the  only  iron  being  the  vertical  ties  and  cast 
iron  angle  blocks  to  take  the  bearing  of  the  timber  struts.  This  makes 
a  very  satisfactory  truss  and  is  quite  economical  where  timber  is  cheap. 


PROBLEM  ipa.     DEAD  LOAD  STRESSES  IN  A  HOWE  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Howe  truss,  span  i62'-o",  panel  length 
i8'-o",  depth  24'-o",  dead  load  600  Ibs.  per  lineal  foot  of  truss.  Calcu- 
late the  dead  load  stresses  by  graphic  resolution.  Scale  of  truss,  i" '  = 
25'-o".  Scale  of  loads,  i"  =  15,000  Ibs. 


PROBLEMS 


461 


Graphic  Statics. 


Problem  19. 


Howe  Truss. 


Graphic  Resolution. 

+75OOO 


vP*       ,,Fi 

w       "    I       M»  •       " 

*20-O  •» 
.: a5  160-0"-- 

Dead  Load=eoo^per  lineal  ft. 

per  trues.        x» 
Joint  Load.rl*  12000* 
5pan,L,  a\6o-ou. 
Panel,l,  =  Eol-o?Q^_ 
Depth,d,: 
N-8. 


6'      \ 


6 


tr 


50 

I 


Truss  -Scale,  i"*E5-oV 

O*        15000*    30000^ 


\ 


^ 


s5cole  of  Loads, i"=i5ooo* 

Dead  Load  Stress  Diagram. 


»Ri 


462  PROBLEMS 

PROBLEM  20.    DEAD  LOAD  STRESSES  IN  A  PRATT  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Pratt  truss,  span   I4o'-o",  panel  length 
2o'-o",  depth  24'-o",  dead  load  800  Ibs.  per  lineal  foot  per  truss.    Cal- 
culate the  dead  load  stresses  by  graphic  resolution.     Scale  of  truss 
i"  =  2o'-o".    Scale  of  loads,  i"  =  16,000  Ibs. 

(b)  Methods. — The  loads  beginning  with  the  first  load  on  the 
left  are  laid  off  from  the  bottom  upwards.     Calculate  the  stresses  by 
graphic  resolution,  beginning  at  R1  and  checking  at  R2,  following  the 
order  shown  in  the  stress  diagram. 

(c)  Results. — The  top. chord  is  in  compression  and  the  bottom 
chord  is  in  tension  as  in  the  Warren  and  Howe  trusses.    The  inclined 
web  members  are  in  tension,  while  the  vertical  posts  are  in  compression. 
Member  1-2  is  simply  a  hanger.    There  is  no  stress  due  to  dead  loads 
in  the  diagonal  members  in  the  middle  panel.     The  stresses  in  the 
posts  are  equal  to  the  vertical  components  of  the  diagonal  members 
meeting  them  on  the  unloaded  chord.     Stresses  in  certain  panels  in 
the  top  and  bottom  chord  are  equal.    The. Pratt  truss  is  quite  generally 
used  for  steel  bridges,  and  is  also  used  for  combination  bridges,  where 
the  tension  members  are  made  of  iron  or  steel  and  the  compression 
members  are  made  of  timber. 


PROBLEM  2oa.     DEAD  LOAD  STRESSES  IN  A  PRATT  TRUSS  BY  GRAPHIC 

RESOLUTION. 

(a)  Problem. — Given  a  Pratt  truss,  span  i6o'-o",  panel  length 
2o'-o",  depth  24'-o",  dead  load  800  Ibs.  per  lineal  feet  per  truss.  Cal- 
culate the  dead  load  stresses  .by  graphic  resolution.  Scale  of  truss 
i"  =  25'-o".  Scale  of  loads,  i"  =  20,000  Ibs. 


PROBLEMS 


463 


Graphic  vStafics.  Problem  ZO. 

Pratt  Truss. 
X      Graphic  Resolution.         X 

+670OO     -+.80000    +60000     +  eOQQO   +67000 


14-0-0 

Dead  Load=soowper  lin.ft. 

per  truss. 
Joini  Load,P, -leooo . 


»60OO*    32OOO      A8OOO* 


<Scale  of  Loads. 


Dead  Load^tress  Diagram 


i 
'Y  ' 

,R 

^, 
i 

Y! 

.*! 

I 
X-)h 

r*\, 

Y! 

^R 


Yi 
I 

R; 

i 

Y-*- 


464  PROBLEMS 

PROBLEM  21.     DEAD  LOAD  STRESSES  IN  A  CAMEL-BACK  TRUSS  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  camel-back   (inclined  Pratt)   truss,  span 
i6o'-o",  panel  length  2o'-o",  depth  at  the  hip  2$'-o",  depth  at  the 
center  32'-o",  dead  load  400  Ibs.  per  lineal  foot  per  truss.     Calculate 
dead  load  stresses  by  graphic  resolution.     Scale  of  truss,  i"  —  25'-o" . 
Scale  of  loads,  i"  =  10,000  Ibs. 

(b)  Methods. — The  loads  beginning  with  the  first  load  on  the  left 
are  laid  off  from  the  bottom  upwards.    Calculate  the  stresses  by  graphic 
resolution,  beginning  at  R^  and  checking  at  R2.     Follow  the  order 
given  in  the  stress  diagram. 

(c)  Results. — The  top  chord  is  in  compression  and  the  bottom 
chord  is  in  tension.     All  inclined  web  members  are  in  tension;  while 
part  of  the  posts  are  in  tension  and  part  are  in  compression.     Member 
1-2  is  simply  a  hanger  and  is  always  in  tension.    This  type  of  truss  is 
quite  generally  used  for  steel  and  combination  bridges  for  spans  from 
150  feet  to  200  feet,  and  also  for  roof  trusses  for  long  span,  where  it 
is  loaded  on  the  top  chord  and  bottom  chord,  or  on  the  top  chord  alone. 


PROBLEM  2ia.     DEAD  LOAD  STRESSES  IN  A  CAMEL-BACK  TRUSS  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  camel-back  (inclined  Pratt)  truss,  span 
i8o'-o",  panel  length  2o'-o"  (three  panels  with  parallel  chords),  depth 
at  the  hip  25'-©",  depth  at  the  center  32'-o",  dead  load  400  Ibs.  per 
lineal  foot  per  truss.  Calculate  dead  load  stresses  by  graphic  resolu- 
tion. Scale  of  truss,  i"  =  2$'-o".  Scale  of  loads,  i"=  12,000  Ibs. 


PROBLEMS 


465 


Graphic  S+atics. 


Problem  21. 


Camel  Back  Truss. 


Dead  Load  =4oo*per  I'm.  ft. 
Joint  Load,F?  =  8ooo? 


Truss^calej'^ss'-o'.'        5 
o         10000       Eooocf* 


Load  >5cale,  i  "=10000* 
Dead  Load  Stress  Diagram. 


466  PROBLEMS 

PROBLEM  22.    WIND  LOAD  STRESSES  IN  A  TRESTLE  BENT. 

(a)  Problem. — Given  a  trestle  bent,  height  45 '-o",  width  at  the 
base  3o'-o",  width  at  the  top  9'-o",  wind  loads  Plf  P2,  F3,  P4,  as  shown. 
Calculate  the  stresses  in  the  members  of  the  bent  due  to  wind  loads  by 
algebraic  moments  and  check  by  calculating  the  stresses  by  graphic 
resolution.    Assume  the  diagonal  members  to  be  tension  members,  and 
that  the  dotted  members  shown  are  not  acting.     Scale  of  truss,  i"  = 
lo'-o".    Scale  of  loads,  i"  =  2000  Ibs. 

(b)  Methods. — (i)  Algebraic  Moments:  To  calculate  the  stresses 
in  the  diagonal  members  take  center  of  moments  about  the  point  A, 
the  point  of  intersection  of  the  inclined  posts.    Then  to  calculate  stress 
in  1-2,  take  section  cutting  1-2,  i-X  and  2-F;  assume  the  external 
force  as  acting  from  the  outside  toward  the  cut  section,  and  we  have 
1-2  X  15.9  +  3000  X  19.3  =  o  and  1-2  =  —  3640  Ibs.    Stresses  in  3-4, 
5-6,  2-3,  4-5  and  6-X  are  found  in  a  similar  manner.    To  obtain  reac- 
tion R!  take  moments  about  (h),  and  R^  X  30  +  2000  X  15  +  2000  X 
30  -f-  3000  X  45  =  o   and    R±  =  +  75oo    Ibs.  =  —  R2.     To    calculate 
stresses  in  2-F,  4-F  and  6-F,  take  moments  about  (b),  (c)  and  (d), 
respectively.     To  calculate  stresses  in  $-X  and  5-X,  take  moments 
about  (f)  and  (g),  respectively.     (2)  Graphic  Resolution:   The  loads 
Ply  P2,  Pz  and  P4  are  laid  off  horizontally  as  shown,  and  with  load  P± 
at  (c)  the  stress  triangle  F-2-4  is  drawn.    The  remainder  of  the  solu- 
tion can  be  easily  followed. 

(c)  Results. — For  the  reason  that  the  wind  may  blow  from  the 
opposite  direction,   both   sets   of   stresses   must  be   considered  in   de- 
signing each  leg. 

PROBLEM  22a.    WIND  LOAD  STRESSES  IN  A  TRESTLE  BENT. 

(a)  Problem. — Given  a  trestle  bent,  height  45'-o",  width  at  the 
base  3o'-o",  width  at  the  top  g'-o",  wind  loads  PIt  P2,  Ps,  P4,  as  shown, 
and  P0  =  3ooo  Ibs.  acting  8'-o"  above  top  of  trestle.  Calculate  the 
stresses  in  the  members  of  the  bent  due  to  wind  loads  by  algebraic 
moments  and  check  by  calculating  the  stresses  by  graphic  resolution. 
Assume  the  diagonal  members  to  be  tension  members,  and  that  the 
dotted  members  shown  are  not  acting.  In  solving  the  stresses  by 
graphic  resolution  continue  the  posts  up  to  the  line  of  P0  and  substi- 
tute an  auxiliary  panel  to  transfer  P0  to  the  bent.  Scale  of  truss,  i"  = 
lo'-o".  Scale  of  loads,  1^  =  3000  Ibs. 


PROBLEMS 


467 


Graphic 


Problem  22. 


2000^ 


4-OOO* 


/  \\<^ 

/       \    \\ 


Y/ 


»Scale,i"=2ooo* 
P,         X       Pa  X      P3    XP*X 


xv< 


*—  - 


3000 


|*9'-0»*      /x°<; 

j/isoodj/7     \    x 


Algebraic  Momenta. 
Center  of  Moments,  A. 

I'EX  15.9  43000  X  19.3=0. 
0     3-4  X 32.0  43000  X\9.34EOOOX34.3^ 


1'- 


(b) 


. 


6~YX  29.25-3000X45-2000X30 
ar(cO    6~ Y=  47 600. 

*- — Center  of  Moments. 


=o.      (h) 


-47500=  - 


468  PROBLEMS. 

PROBLEM  23.     STRESSES  IN  THE  PORTAL  OF  A  BRIDGE  BY  ALGEBRAIC 
MOMENTS  AND  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  portal  of  a  bridge  of  the  type  shown, 
inclined  height  30'  o",  center  to  center  width  15'  o",  load  R==  2,000 
Ibs.,  end-posts  pin-connected  at  the  base.  Calculate  the  stresses  by 
algebraic  moments  and  check  by  graphic  resolution.  Scales  as  shown. 

(&)  Methods.— Now  H  =  H'=i,ooo  Ibs.  V=—V,  and  by 
taking  moments  about  B,  V = 30  X  2,000/1 5 =4,000  Ibs.  —  — V. 

'Algebraic  Moments. — In  passing  sections,  care  should  be  used  to 
avoid  cutting  the  end-posts  for  the  reason  that  these  members  are  sub- 
ject to  bending  stresses  in  addition  to  the  direct  stresses.  To  calcu- 
late the  stress  in  member  $-Y  take  the  center  of  moments  at  joint  (i) 
and  pass  a  section  cutting  members  4~bf  3-4  and  $-Y,  and  cutting  the 
portal  away  to  the  left  of  the  section.  Then  assumes  stress  3-F  as  an 
external  force  acting  from  the  outside  toward  the  cut  section,  and  $-Y 
X  10  X  0.447  (sin0)  -\-H  X  30'  =  o.  The  stress  in  3~F=  —  6,710 
Ibs.  The  remaining  stresses  are  calculated  as  shown. 

Graphic  Resolution. — Lay  'off  a-A—A-b  =  H  —  i,ooo  Ibs.,  and 
.'A-Y=V'  =  4,000  Ibs.  Then  beginning  at  point  B  in  the  portal  the 
force  polygon  for  equilibrium  is  Or-A-Y-i'-a,  in  which  I'-a  is  the 
stress  in  the  auxiliary  member  i-a,  and  F-i'  is  the  stress  in  the  post 
1-Y  when  the  auxiliary  member  is  acting.  The  true  stress  in  i-Y  is 
equal  to  the  algebraic  sum  of  the  vertical  components  of  the  stress 
I '-a  and  Y-i',  and  equals  F'  = — 4,000  Ibs.  Next  complete  the  force 
triangle  at  the  intersection  of  the  auxiliary  members.  Stress  i'-a  is 
known  and  the  force  triangle  is  o-i'-2'-a,  the  forces  acting  as  shown. 
The  stress  diagram  is  carried  through  in  the  order  shown,  checking  up 
at  the  point  A.  The  correct  stresses  are  shown  by  the  full  lines  in 
the  stress  diagram.  The  true  stress  in  3-2  will  produce  equilibrium 
for  vertical  stresses  at  joint  (i)  as  shown.  The  maximum  shear  in 
the  posts  is  H=i,ooo  Ibs.  The  maximum  bending  moment  in  the 
posts  will  occur  at  the  foot  of  the  member  3~F,  joint  (3),  and  is 
Af  =  1,000  X  20  X  12  =  240,000  in.-lbs. 

(c)  Results. — The  method  of  graphic  resolution  requires  less 
work  and  is  more  simple  than  the  method  of  algebraic  moments. 

Note:  The  portal  is  not  pin-connected  at  joints  (3)  and  the  corre- 
sponding joint  on  the  opposite  side,  as  might  be  inferred  from  the 
figure. 


PROBLEMS. 


469 


Graphic  5batics 

Stresses 


Problem  ?3. 
in  a  Portal.  ,&.{&'. 

U_5/^J</5'^J</5/_>J 
@k  1-3000  |/4 1000  \f+5000\  R=20OO 


- 10*0.447  =~e?l° 
2000*5+1000*25-  V*2  S*  it  -  < 


+5000 


4.47 
=-2270 
5000*WOOO*W-4000*I5 


5*OM4 

=  -4470 
1000*50-4000*5 

5 
=-2000 


\ 
\ 

A 


i«J^ 


^-H 


Scale  of  Portal 

0'           7'6" 
Y    ' '    r 


Tan  6 =0.500 
Cos 6-  0.834 


/•/ 


V=-400O 


©7-Y-- 


jT 
1000*50-4000*10 


v  1000*50       s-7,n 
-Y*  •//)„/,  ^^v  =  ^7/^ 


10*0.447 
4000*10-1000*30 

10*0.447 

^2270 

5cale  of  Loads 
0*    2000*      4000 


5fress 
Diagram 


PROBLEM  23 A.     STRESSES  IN  THE  PORTAL  OF  A  BRIDGE  BY  ALGEBRAIC 
MOMENTS  AND  GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  the  portal  shown  in  Problem  23,  except  that 
the  posts  are  fixed  at  their  bases.  Calculate  the  stresses  by  algebraic 
moments  and  check  by  graphic  resolution.  Assume  the  point  of  contra- 
flexure  as  half  way  between  the  base  of  the  post  and  the  foot  of  the 
knee  brace.  Scales  as  in  Problem  23. 


470  PROBLEMS. 

PROBLEM  24.    WIND  LOAD   STRESSES  IN  A  TRANSVERSE   BENT   BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  transverse  bent,  span  40'  o,"  pitch  of  roof 
J,  height  of  posts  20'  o",  posts  pin-connected  at  the  base,  wind  load  20 
Ibs.  per  square  foot  of  vertical  projection.     Calculate  the  wind  load 
stresses  in  the  bent  by  graphic  resolution.     Scale  of  bent,  i"  =  10'  o". 
Scale  of  loads,  i"  =  3,000  Ibs. 

(b)  Methods.— Now//  =  JSP= 4,500  Ibs.  =  H'.    To  calculate  V 
take  moments  about  the  foot  of  the  right-hand  post,  and  FX4o' — 
3,PooXi34'—  1,750X20'  —  1,500X25'  —  750  X3o'  =  o.      Then    V 
=  +3,375  Ibs.— P. 

To  construct  the  stress  diagram  lay  off  the  load  line  Px  +  P2  +  P3 
+  P4  +  P6,  and  i-F=  7  =  3,375  Ibs.  Beginning  at  the  foot  of  the 
windward  post,  V  acts  downward,  H  —  X-i  acts  to  the  left,  P6  acts 
to  the  right.  The  polygon  is  closed  by  drawing  lines  parallel  to  i-X 
and  i-F,  the  final  stress  polygon  being  Y-i-X-X-i'.  Then  pass  to  the 
load  P4  in  the  transverse  bent,  and  in  the  stress  diagram  P4  acts  to  the 
right,  i-X  acts  upwards  to  the  left,  1-2  acts  to  the  right,  and  2-X 
acts  downwards  to  the  left,  closing  the  polygon.  The  remainder  of  the 
stress  diagram  is  drawn  in  a  similar  manner,  passing  to  the  foot  of 
the  Jmee  brace,  then  to  the  top  of  the  post,  etc.,  finally  checking 
up  at  the  foot  of  the  leeward  post.  The  maximum  shear  is  in  the  lee- 
ward post,  below  the  knee  brace  the  shear  is  H= 4,500  Ibs.,  above  the 
knee  brace  the  shear  is  the  horizontal  component  of  the  stress  in  IO-X 
=  io'-X= 9,000  Ibs.  The  maximum  bending  moment  in  the  post  is  at 
the  foot  of  the  leeward  knee  brace  and  is  M= 4,500  X  134  =  60,000 
ft.-lbs.  For  further  explanation  see  the  author's  "The  Design  of 
Steel  Mill  Buildings." 

(c)  Results. — The  stresses  in  the  members  do  not  follow  the  usual 
rules  for  trusses  loaded  with  vertical  loads ;  the  top  chord  is  partly  in 
tension  and  partly  in  compression,  while  the  bottom  chord  is  in  com- 
pression.    The  bent  should  be  designed  for  the  wind  load  stresses  com- 
bined with  the  dead  load  and  the  minimum  snow  load  stresses,  for  the 
wind  load  and  the  dead  load  stresses,  or  for  the  wind  load  and  the 
dead  load  stresses,  whichever  combination  produces  maximum  stresses 
or  reversals  of  stresses. 

The  stresses  in  the  posts  are  calculated  by  dropping  the  points  i,  2, 
io  and  II  to  the  points  i',  2',  10'  and  n',  respectively,  on  the  load  line, 
or  on  load  line  produced.  The  stresses  in  the  windward  post  are  i'—Y 
and  2'~3,  while  the  stresses  in  the  leeward  post  are  n'-Y  and  9-10'. 
The  maximum  shear  in  the  leeward  post  is  above  the  knee  brace  and 
is  lo'-X  =  9,000  Ibs. 


PROBLEMS. 


471 


Graphic  Statics  Problem  c?4. 

Wind  Load  Stresses  -Transverse  Bent 

P,*750 

X     S&^^^      ~  X~        ~t  Hind  load 20*per3q. 
•  tem&r%  :  *:^^_  5  ^  Vertlcalpr0jecf;0n 


P5=_zooo\ 


Y  Pifch  Y 

^  :  Span 40, Height  10    ^ 

**?*— Jt-  frnh  spaced  15'c.ioc.  * 


5ca/e  of  Bent 
0       y     10'  zo 


r  .+-m*io=mo 

/  P5~-500*6j=2000* 
/    H=H'=4500* 


-5375 


T 


K *%^2 

|V     /* 

H--\^--H 

i  xxx 

i^VAk- 


Wind  Load  5fre$5  Diagram 


PROBLEM  24A.     WIND  LOAD  STRESSES  IN  A  TRANSVERSE  BENT  BY 
GRAPHIC  RESOLUTION. 

(a)  Problem. — Given  a  transverse  bent,  span  40'  o",  pitch  of  roof 
J,  height  of  posts  20'  o",  posts  pin-connected  at  the  base,  wind  load  20 
Ibs.  per  square  foot  normal  to  the  sides  and  the  normal  component  of 
a  horizontal  wind  load  of  30  Ibs.  per  square  foot  on  the  roof.  (The 
normal  load  on  the  roof  for  a  horizontal  wind  load  of  30  Ibs.  is  22^  Ibs. 
per  sq.  ft.,  see  "Steel  Mill  Buildings.")  Calculate  the  wind  load 
stresses  in  the  transverse  bent  by  graphic  resolution.  Scale  of  bent, 
i"=  10'  o".  Scale  of  loads,  i"  =  3ooo  Ibs. 


INDEX. 


Algebraic  calculation  of  stresses — see 
Stresses. 

Allowable   sections    329 

Anchorage  of  columns   115 

Anti-condensation  roofing    241 

Arch — see     Two-hinged     and     three- 
hinged  arches. 

Asbestos   roofing    258 

Asphalt  paint    339 

Asphalt  roofing    257 

A.  T.  &  S.  F.  Locomotive  Shops   . . .  367 

Beams,  Graphic  Methods  for  calcula- 
ting the  deflection  of   158 

Bearing  power  of  piles   273 

Bearing  power  of  soils    272 

Bending  moment  in  beams,  33,  56,  57,  59 

Boyer   plant    185 

Bracing    92 

Brick   arch   floors    290 

Brick   floors    290 

Bridge  trusses,  stresses  in 

Camel   Back    72 

Pratt 69 

Warren    67 

Also,  see  Stresses. 

Brown  &  Sharpe  foundry   184 

"  Buckeye  "  flooring    294 

Buckled  plates    296 

Carbon   paint    333 

Carey's  roofing 259 

Center  of  gravity    34 

Cement   floors    282 

Choice  of  sections    328 

Circular   ventilators    320 

Cleaning  the  surface  of  steel   336 

Coal-tar   paint    339 


Columns 

Design  of    217 

Details  ...205,  206,  207,  208,  209,  380 

Pressure  on  masonry    278 

Types  of   203 

Combined  stresses 143 

Compression  and  cross  bending 145 

Tension  and  cross  bending   148 

Stress  in  bars  due  to  weight 149 

Diagram  for  stress  in  bars  due  to 

weight    149 

Concentrated  moving  loads 61 

Concentrated  load  shear   56 

Concentrated  load  stresses   53 

Concrete   buildings    268 

Concrete  slabs    266 

Conkey  printing  plant    184 

Continuous  beams   164 

Corrosion  of  steel 330 

Corrugated  floor    295 

Corrugated  steel 

Anti-condensation  lining   241 

Corner  finish    234 

Cornice     237-241 

Cost   of    244 

Details     232 

Diagram  for  safe  loads   230 

Flashing     233 

Fastening     225 

Gutters  and  Conductors 23^ 

Design  of    235 

Plans    244 

Plans  for  transformer   243 

Roofing     246 

Rotary  shear  for  cutting   227 

Ridge  roll   232 

Standard  sheets   226 


473 


474 


INDEX 


Steel    lists    for    transformer    build- 
ing     243 

Strength  of 230 

Tests   of    231 

Weight  of    8,  225 

Cost — see  estimate  of  cost,  and   cost 
under  different  items. 

Estimate  of   34$,  349 

Of  miscellaneous  materials   355 

Standard  hardware  lists    357 

Of   material    35i 

Of  mill  details  and  shop  work  ....  353 

Crane    girders    224 

Details   of    380,  382 

Deflection  of  beams   158 

Deformation   diagram  134 

Design — see  Article  for  which  design 
is  wanted. 

Details — see  Article  for  which  details 
are  wanted. 

Diagram    for    stress    in    bars    due    to 
their   own  weight    149 

Diffusion  of  light   299 

Doors 

Paneled    322 

Wooden    322 

Sandwich     323  * 

Steel   323 

Details  for   325 

Cost  of    325 

Draw  bridges,  reactions   of    169 

Fastening  corrugated  steel    227 

Ferroinclave 260,  295 

Finishing  coat  of  paint   338 

Floors     281 

Brick    284 

Brick   arch    290 

Buckled  plates    296 

"  Buckeye  "  fireproof    294 

Cement  282 

Corrugated    295 

Corrugated  iron  arch   291 

Expanded  metal 292 

Ferroinclave    295 

Roebling    293 


Multiplex  steel  295 

Steel   plates    296 

Tar   concrete    284 

Wooden    282 

Floor  beam  reaction,  Maximum    ....    81 

Foundations 

Bearing  power  of  piles    273 

Bearing  power  of  soils    272 

Design  of  footings   278 

Pressure  of  walls  on  foundation  ..275 
Pressure  of  pier  on  foundation  ...276 
Pressure  of  column  on  masonry  ..278 

Girders,   crane    224 

Girders,   design   of    221 

Glass 

Amount  of  light  required   310 

Cost   of    304 

Details  of  windows    307 

Diffusion  of  light   299 

Double  glazing 307 

Kinds  of   298 

Factory  ribbed   299 

Maze 299 

Plane    298 

Plate 298 

Prisms    299 

Ribbed    299 

Wire   299 

Window    298 

Relative  value  of  different  kinds   ..299 

Placing  the  glass    302 

Size   of    304 

Window  shades   303 

Government   Building,    St.    Louis   Ex- 
position     385 

Granite   roofing    259 

Graphic  equation  of  elastic  curve   ...158 

Gravel   roofing    254 

Ground    floors    281 

Hardware  lists    357,  3$8 

Influence  diagram    77 

Iron    oxide    333 

Iron,   classification 352 

Iron,       corrugated — see       Corrugated 
steel. 


INDEX 


475 


Lead    33* 

Linseed  oil    331 

Lists,  standard  hardware 357,  358 

Loads 

Dead   loads  4 

Weight  of  covering    8 

Weight  of  cranes    18 

Weight  of  girts   8 

Miscellaneous  material 19 

Weight  of  purlins   8 

Weight  of  structure   9 

Loads  on  simple  roof  trusses  ...   47 

Concentrated  live  loads   21 

Snow   loads    10 

Wind   loads    12 

Miscellaneous   loads    17 

Live  loads  on  floors   17 

Locomotive  shops 

A.  T.  &  S.  F 197,  367 

Oregon  Short  Line   195 

Philadelphia  &  Reading   372 

St.  L.  I.  M.  &  S 196 

Union  Pacific   196 

Methods  of  calculations 

Algebraic  moments    44,   72 

Algebraic   resolution    40,  65 

Graphic  moments   46,  73 

Graphic  resolution    42,  70 

Also — see   Stresses. 

Mill  buildings 

General  design  of   175 

Specifications    for    391 

Types    i 

Masonry  walls    3 

Masonry  filled  walls 2 

Steel  frame   i 

Miscellaneous  loads 

Live  loads  on  floors   17 

Weight  of  electric  cranes    18 

Weight  of  hand  cranes    18 

Weight  of  miscellaneous  material..    19 

Miscellaneous    structures 

A.  T.  &  S.  F.  shops    197,  367 

Government     Building,     St.     Louis 

Exposition   385 

Philadelphia  &  Reading  shops   ....  372 

32 


Reinforced     concrete     round-house 

for  Canadian  Pacific  R.  R 388 

St.  Louis  Coliseum   362 

Steam         Engineering         Buildings 

Brooklyn  Navy  Yard   381 

Steel  Dome  West  Baden  Hotel   ...359 

Mixing  paint    334 

Modified  saw-tooth  roof    186 

Moment  of  inertia  of  areas   38 

Moment  of  inertia  of  forces 35 

Culmann's   method    35 

Mohr's   method    36 

Moments 

Algebraic   44,   56,  57,  72 

Graphic    32,  46,  56,  57,  73 

Moments  in  beams 

Concentrated  loads    56 

Concentrated  moving  loads    59 

Maximum  moment  in  a  truss 77 

Uniform  loads    57 

Uniform   moving  loads    59 

Monitor   ventilators 317 

Moose  Jaw  Round-house 388 

Multiplex  steel  floor 295 

Oil,  linseed 331 

Oil,   paint    330 

Paint 

Applying   the    335 

Asphalt    339 

Carbon    333 

Cement  paint    339 

Cleaning  the  surface    336 

Coal-tar   paint    339 

Cost   of    336 

Covering  capacity    334 

Finishing  coat    338 

Iron   oxide    333 

Lead    332 

Linseed  oil    331 

Mixing  the    334 

Oil  paints    330 

Priming   coat    337 

Proportions    334 

References  on  paint   340 

Zinc    .  333 


INDEX 


Painting 

Applying  the  paint    335 

Cost   of    337 

Cleaning  the  surface 336 

Paneled  doors    322 

Philadelphia  &  Reading  shops    372 

Pins,  stresses  in    154 

Pitch  of  roof   191 

Pitch   of  trusses    192 

Plate  girders    221 

Polygon 

Equilibrium     26 

Force    24 

Moment   56,  57,  59,  61,  73 

Shear  56,  57,  59,  61,  74 

Portals 

Anchorage  of  columns   115 

Stresses  in 

Continuous  portals    117 

Double  portal 118 

Simple  portals,  columns  hinged 

Algebraic  solution    no,   112 

Graphic   solution    112 

Simple  portals,  columns  fixed 

Algebraic  solution   115 

Graphic  solution    117 

Portland  cement  paint   339 

Pressure  of  columns  on  masonry  . .  .  .278 

Pressure  of  pier  on  foundation 275 

Pressure  of  wall  on  foundation 276 

Proportions  of  paint  and  oil 334 

Purlins   _ 213 

Reactions  of 

Beams   29,   55 

Cantilever  truss 30 

Draw  bridges   159 

Overhanging  beam    55 

Three-hinged  arch   120,  121 

Transverse  bent 103 

Two-hinged  arch   128,  131,  133 

Resolution 

Algebraic    40,  65 

Graphic 42,   70 

Red  lead    332 

Reinforced  round-house  388 

References  on  paint  and  painting  ...340 


Roebling  floor    293 

Roof,  pitch  of   191 

Roof  trusses — see  Trusses. 
Stress  in — see  Stresses. 

Roof  coverings  for  railway  buildings. 261 

Roofing, 

Asbestos   185,  258 

Asphalt    257 

Carey's     259 

Corrugated   steel    246 

Cost  of   246,  262 

Examples    of    261 

Ferroinclave    260 

Granite    259,  262 

Gravel   254,  262 

Paroid    262 

Ruberoid 259,  262 

Slag .. 256,   375 

Sheet  steel   253,  262 

Slate   247,  262 

Sparham   261,  262 

Tile    250,   261,   262 

Round-house    388 

Ruberoid  roofing   259 

Saw-tooth  roofs.    177,  183,  184,  185,  186, 
187,  188,  189,  190,  202,  368,  369 

Boyer  plant    185 

Brown  &  Sharpe  foundry    184 

Conkey  printing  plant    184 

Ingersoll-Sargent  Drill  Co 187 

Ketchum's   modified    186 

Locomotive  shop   190 

Louisville  &  Nashville  R.  R.  shops,  187 

Matthiessen  &  Hegeler  shops   202 

P.  &  L.  E.  R.  R.  shop 188 

Sections,  choice  of   328 

Shear  in  beams,  for 

Concentrated  loads    56 

Concentrated  moving  loads 61 

Maximum  shear  in  a  truss 79 

Uniform  moving  loads 59 

Shear   polygon — see    Polygon. 

Sheet  steel  roofing    253 

Shingle  roofs   258 

Shop  cost    353 

Shop  costs,  actual 355 


INDEX 


477 


Side  walls 

Concrete  slabs    266 

Corrugated   steel    263 

Expanded  metal  and  plaster 263 

Masonry  walls   267 

Thickness   of    267 

Skylights   303 

Details  of    307 

Slate   roofing 247 

Slag   roofing    256,   375 

Snow  loads   10 

Sparham  roofing    261 

Specifications    for    Steel    Frame    Mill 

Buildings — Appendix  1 391 

Standard  hardware  lists    357,  358 

Steam      engineering      buildings      for 

Brooklyn  Navy  Yard    381 

Stress  in  bars  due  to  weight 149 

Stresses,   allowable    1 78,   214 

Also — see  Appendix  1 391 

Stresses  in 

Bracing    92 

Bridge  trusses — see  Trusses, 
Portals — see  Portals. 
Roof  trusses — see  Roof  trusses. 
Transverse     bent — see     Transverse 

bent. 

Three-hinged       arch — see       Three- 
hinged  arch. 
Two-hinged    arch — see    Two-hinged 

arch. 
Stresses 

Calculation   of    22 

Combined    144 

Eccentric    152 

Struts  and  bracing   213 

Tar  concrete  floors   284 

Three-hinged  arch 

Calculation  of  stresses 120 

Dead  load 122 

Reactions^ 

Algebraic  method    1 20 

Graphic  method   121 

Wind  load  stresses  125 

Timber  floors   285,  290 

Tile  roofing 250 


Tin   roofs    251 

Translucent*  fabric    306 

Cost  of    307 

Transverse  bent 

Details    200,  202 

Transverse  bent,  stresses  in 

Dead  load    83,  94 

Maximum   91,   101 

Snow   load 83 

Wind  load 

Algebraic  calculation    84 

Columns  fixed    87 

Columns  hinged    84,   168 

Graphic  calculation 

Case  2    96 

Case  3    98 

Case  4    99 

Case  5    104 

Graphic  calculation  of  reactions,  103 
Transverse  bent  with  side  sheds  ....105 
Transverse  bent  with  ventilator  ....103 
Trusses 

Economic  spacing  of   192 

Design  of    214 

Details  of   197,  199,  378 

Pitch   of    190 

Saw-tooth — see  Saw-tooth  roofs. 

Types    180,    190 

Trusses,  stresses 
Bridge  trusses 

Algebraic   moments   72 

Algebraic  resolution   65 

Graphic   moments    73 

Graphic   resolution    70 

Roof  trusses 

Algebraic  moments   44 

Algebraic  resolution   40 

Graphic  moments 46 

Graphic   resolution    42 

Concentrated  load 53 

Dead  load 47 

Dead  and  ceiling  load 48 

Snow  load 49 

Wind  load 49,  50,  51 

Two-hinged  arch 

Design  of    141 

Two-hinged  arch,  stresses 


478 


INDEX 


Calculation  of  reactions    128 

Algebraic  solution   131 

Graphic  solution    133 

Dead  load   i3S 

Dead  and  wind  load    137 

Temperature  stresses    140 

With   horizontal   tie 1 39 

Ventilators 3*7 

Monitor    317 

Cost  of    320 

Circular    320 

Cost  of    321 

Walls,  masonry    267 

Walls,  side   263 


Weight,  estimate  of   341 

Weight  of  building  materials   20 

Weight  of  merchandise    20 

West   Baden   dome    359 

Window  shades    303 

Windows 

Amount  of  light    310 

Cost  of    304 

Details  of    307,   312 

Double   glazing    307 

Glass — see  Glass. 

Wooden  doors    312 

Wooden  floors    285 

Zinc   paint    333 


APPENDIX  III 

STRUCTURAL  DRAWINGS,  ESTIMATES  AND 

DESIGNS. 

PREFACE. 

The  aim  in  preparing  these  notes  has  been  to  give  simple  and  direct  instruc- 
tions for  preparing  structural  drawings,  estimates  and  designs.  While  most 
bridge  companies  furnish  their  draftsmen  with  similar  information,  the  notes 
are  usually  prepared  in  blue  print  form  and  are  not  available  for  the  use  of 
the  student  and  independent  engineer. 

In  preparing  these  notes  the  instructions  of  many  bridge  companies  have 
been  consulted ;  special  credit  being  due  the  instructions  prepared  by  the 
American  Bridge  Company,  the  McClintic-Marshall  Construction  Company, 
and  the  Pennsylvania  Steel  Company. 


TABLE  OF  CONTENTS. 

PACK 

CHAPTER   I. 

Plans  of  Structures  2  to  3 

CHAPTER   II. 

Structural  Drawings    3  to  32 

Methods — Rules  for  Shop  Drawings — Plate  Girder  Bridges — 
Truss  Bridges — Office  Buildings  and  Steel  Frame  Buildings — 
Detail  Notes — Rules  for  Ordering  Material — Plates  and  Shapes 
Most  Easily  Obtained. 

CHAPTER   III. 

Estimates  of  Structural  Steel  32  to  44 

General  Instructions — Mill  Buildings — Office  Buildings — Truss 
Bridges — Taking  off  Material — Card  of  Mill  Extras — Corru- 
gated Steel. 

CHAPTER   IV. 

Design    of    Steel    Structures    44  to  48 

General  Instructions — Mill  Buildings — Plate  Girders — Truss 
Bridges. 

CHAPTER   V. 

Tables  and  Structural  Standards   48  to  78 

i 


CHAPTER   I. 
PLANS  FOR  STRUCTURES. 

Introduction. — The  plans  for  a  structure  must  contain  all  the  information 
necessary  for  the  design  of  the  structure,  for  ordering  the  material,  for  fabri- 
cating the  structure  in  the  shop,  for  erecting  the  structure,  and  for  making  a 
complete  estimate  of  the  material  used  in  the  structure.  Every  complete  set 
of  plans  for  a  structure  must  contain  the  following  information,  in  so  far  as  the 
different  items  apply  to  the  particular  structure. 

1.  General  Plan. — This  will  include  a  profile  of  the  ground;  location  of 
the  structure;  elevations  of  ruling  points  in  the  structure;  clearances;  grades; 
(for  a  bridge)  direction  of  flow,  high  water,  and  low  water;  and  all  other  data 
necessary  for  designing  the  substructure  and  superstructure. 

2.  Stress  Diagram. — This  will  give  the  main  dimensions  of  the  structure, 
the  loading,  stresses  in  all  members  for  the  dead  loads,  live  loads,  wind  loads, 
etc.,  itemized  separately;  the  total  maximum  stresses  and  minimum  stresses; 
sizes  of  members;  typical  sections  of  all  built  members  showing  arrangement 
of  material,  and  all  information  necessary  for  the  detailing  of  the  various  parts 
of  the  structure. 

3.  Shop  Drawings.— Shop  detail  drawings  should  be  made  for  all  steel  and 
iron  work  and  detail  drawings  of  all  timber,  masonry  and  concrete  work. 

4.  Foundation  or  Masonry  Plan.— The  foundation  or  masonry  plan  should 
contain  detail  drawings  of  all  foundations,  walls,  piers,  etc.,  that  support  the 
structure.    The  plans  should  show  the  loads  on  the  foundations;  the  depths  of 
footings;  the  spacing  of  piles  where  used;  the  proportions  for  the  concrete; 
the  quality  of  masonry  and  mortar;  the  allowable  bearing  on  the  soil;  and  all 
data  necessary  for  accurately  locating  and  constructing  the  foundations. 

5.  Erection    Diagram. — The    erection    diagram    should    show   the    relative 
location  of  every  part  of  the  structure;   shipping  marks  for  the  various  mem- 
bers; all  main  dimensions;  number  of  pieces  in  a  member;  packing  of  pins; 
size  and  grip  of  pins,  and  any  special  feature  or  information  that  may  assist 
the  erector  in  the  field.    The  approximate  weight  of  heavy  pieces  will  materially 
assist  the  erector  in  designing  his   falsework  and  derricks. 

6.  Falsework  Plans. — For  ordinary  structures  it  is  not  common  to  pre- 
pare falsework  plans  in  the  office,  this  important  detail  being  left  to  the  erector 
in  the  field.     For  difficult  or  important  work  erection  plans  should  be  worked 
out  in  the  office,  and  should  show  in  detail  all  members  and  connections  of  the 
falsework,  and  also  give  instructions  for  the  successive  steps  in  carrying  out 
the  work.     Falsework  plans  are  especially  important  for  concrete  and  masonry 

2 


STRUCTURAL    DRAWINGS.  3 

arches  and  other  concrete  structures,  and  for  forms  for  all  walls,  piers,  etc. 
Detail  plans  of  travelers,  derricks,  etc.,  should  also  be  furnished  the  erector. 

7.  Bills    of   Material. — Complete   bills   of   material    showing   the   different 
parts  of  the  structure  with  its  mark,  and  the  shipping  weight  should  be  prepared. 
This  is  necessary  in  checking  up  the  material  to  see  that  it  has  all  been  shipped 
or  received,  and  to  check  the  shipping  weight. 

8.  Rivet  List. — The  rivet  list  should  show  the  dimensions  and  number  of 
all  field  rivets,  field  bolts,  spikes,  etc.,  used  in  the  erection  of  the  structure. 

9.  List  of  Drawings. — A  list  should  be  made  showing  the  contents  of  all 
drawings  belonging  to  the  structure. 


CHAPTER   II. 
STRUCTURAL  DRAWINGS. 

METHODS.— The  drawings  for  structural  steel  work  differ  from  the  draw- 
ings for  machinery  in  that  (a)  two  scales  are  used,  one  for  the  length  of  the 
member  or  the  skeleton  of  the  structure,  and  one  for  the  details;  (b)  members 
are  commonly  shown  by  one  projection;  and  (c)  the  drawings  are  not  to 
exact  scale,  all  distances  being  governed  by  figures. 

Two  methods  are  used  in  making  shop  drawings. 

(1)  The  first  method  is  to  make  the  drawings  so  complete  that  the  templets 
can  be  made  for  each  individual  piece  on  the  bench.    This  method  is  used  for 
all  large  trusses  and  members,  and  where  there  is  not  room  to  lay  the  member 
out  on  the  templet  shop  floor.    The  details  for  the  joint  of  a  Fink  roof  truss 
completely  detailed  are  shown  in  Fig.  I.    A  joint  of  a  roof  truss  of  the  loco- 
motive shop  of  the  A.  T.  &  S.  F.  R.  R.,  at  Topeka,  Kansas  is  completely  de- 
tailed in  Fig.  2. 

(2)  The  second  method  is  to  give  on  the  drawings  only  sufficient  dimen- 
sions to  locate  the  position  of  each  member,  the  number  of  rivets,  and  the  sizes 
of  members,  leaving  the  details  to  be  worked  out  by  the  templet  maker  on  the 
laying-out  floor.  Sufficient  data  should  be  given  to  definitely  locate  the  main 
laying-out  points.     The  interior  pieces  should  be  located  by  center  lines  corre- 
sponding to  the  gage  lines  of  the  angles,  or  center  line  of  the  piece,  as  the  case 
may  be.     The  rivet  spacing  should  be  given  complete  for  members  detailed  on 
different  sheets,  or  where  it  is  necessary  to  obtain  a  required  clearance,  and 
other  places  where  it  will  materially  assist  the  templet  maker.     The  drawings 
should  indicate  the  number  and  arrangement  of  the  rivets  in  each  connection, 
as  well  as  the  maximum,  the  usual  and  the  minimum  rivet  pitch  allowed.    Sketch 
details  of  the  joint  which  was  completely  detailed  in  Fig.  I  are  shown  in  Fig.  3, 
and  the  outline  details  of  a  roof  truss  by  the  second  method  are  shown  in 
Fig.  4- 

Members  may  be  detailed  in  the  position  which  they  are  to  occupy,  or  they 
may  be  detailed  separately.  For  riveted  trusses  and  riveted  members  the 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


FIG.  I.    TRUSS  JOINT,  COMPLETELY   DETAILED. 


entire  truss  or  member  should  be  detailed  in  position.  The  detail  shop  plans 
for  a  riveted  brace  are  shown  in  Fig.  5.  The  field  rivets  are  shown  by  black 
and  the  shop  rivets  by  open  circles.  The  center  lines  are  indicated  by  dotted 
lines.  Light  full  black  lines  are  commonly  used  for  dimension  lines,  while  red 
dimension  lines  are  sometimes  used  but  do  not  make  as  good  blue  prints  as 
black  lines. 

RULES  FOR  SHOP  DRAWINGS. 

The  following  rules  are  essentially  those  in  use  by  the  best  bridge  and 
structural  shops. 

Size  of  Sheet. — The  standard  size  of  sheet  shall  be  24  X  36  in.  with  two 
border  lines  y^  and  I  in.  from  the  edge  respectively,  see  Fig.  6.  Sheets  18  X  24 
in.  with  two  border  lines  y2  and  I  in.  from  the  edge  respectively,  may  also  be 
used.  For  beam  sheets,  bills  of  material,  etc.,  use  letter  size  sheets  8l/2  X  n  in. 


STRUCTURAL    DRAWINGS.  5 

Title. — The  title  shall  be  arranged  uniformly  for  each  contract  and  shall 
be  placed  in  the  lower  right  hand  corner.  The  title  shall  contain  the  name  of 
the  job,  the  description  of  the  details  on  the  sheet,  the  number  of  the  sheet, 
spaces  for  approval  and  other  information  as  shown  in  Fig.  6. 


FIG.  2.    JOINT  OF  ROOF  TRUSS  COMPLETELY  DETAILED. 

of  Roof  Truss.) 


(Section  of  Shop  Details 


Scale.  —  The  scale  of  the  lengths  of  the  members  or  skeleton  of  the  struc- 
ture shall  be  ^,  or  ^,  or  ^  in.  to  i  ft.,  depending  upon  the  available  space 
and  the  complexity  of  the  member  or  structure.  Shop  details  shall  as  a  rule  be 
made  Y$  or  i  in.  to  i  ft.  For  small  details  1^2  and  3  in.  to  i  ft.  may  be  used; 
while  for  large  plate  girders  ^  or  ^  in.  to  i  ft.  may  be  used. 


6  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

Views  Shown. — Drawings  shall  be  neatly  and  carefully  made  to  scale. 
Members  shall  be  detailed  in  the  position  which  they  will  occupy  in  the  struc- 
ture; horizontal  members  being  shown  lengthwise,  and  vertical  members  cross- 
wise on  the  sheet.  Inclined  members  (and  vertical  members  when  necessary 


FIG.  3.    TRUSS  JOINT,  SKETCH  DETAILED. 

on  account  of  space)  may  be  shown  lengthwise  on  the  sheet,  but  then  only  with 
the  lower  end  on  the  left.  Avoid  notes  as  far  as  possible;  where  there  is  the 
least  chance  for  ambiguity,  make  another  view. 

In  truss  and  girder  spans,  draw  the  inside  view  of  the  far  truss,  left  hand 
end,  Fig.  7.  The  piece  thus  shown  will  be  the  right  hand,  and  need  not  be 
marked  right.  In  cases  where  it  is  necessary  to  show  the  left  hand  of  a  piece, 
mark  "left-hand  shown"  alongside  the  shipping  mark. 

Show  all  elevations,  sections  and  views  in  their  proper  position,  looking 
toward  the  member.  Place  the  top  view  directly  above,  and  the  bottom  view 
directly  below  the  elevation.  The  bottom  view  should  always  consist  of  a  hori- 
zontal section  as  seen  from  above. 

In  sectional  views,  the  web  (or  gusset  plate)  shall  always  be  blackened; 
angles,  fillers,  etc.,  may  be  blackened  or  cross-hatched,  but  only  when  necessary 
on  account  of  clearness.  In  a  plate  girder,  for  example,  it  is  -not  necessary  to 
blacken  or  cross-hatch  all  the  fillers  and  stiffeners  in  the  bottom  view. 

Holes  for  field  connections  shall  always  be  blackened,  and  shall,  as  a  rule, 


STRUCTURAL    DRAWINGS. 


be  shown  in  all  elevations  and  sectional  views.    Rivet  heads  shall  be  shown  only 
where  necessary;  for  example,  at  the  ends  of  members,  around  field  connections, 


f 

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I 

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j  V  ! 
i  A4 

i    i 

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-a-   *    4 

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avm 

8  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

when  countersunk,  flattened,  etc.  In  detailing  members  which  adjoin  or  connect 
to  others  in  the  structure,  part  of  the  latter  shall  be  shown  in  dotted  lines,  or  in 
red,  sufficiently  to  indicate  the  clearance  required  or  the  nature  of  the  connec- 
tion. Plain  building  work  is  exempted  from  this  rule. 


FIG.  5.     SHOP   DETAILS  OF   BRACE. 


A  diagram  to  a  small  scale,  showing  the  relative  position  of  the  member  in 
the  structure,  shall  appear  on  every  sheet,  Fig.  8  and  Fig.  9.  The  members 
detailed  on  the  sheet  shall  be  shown  by  heavy  black  lines,  the  remainder  of  the 
structure  in  light  black  lines.  Plain  building  work  is  exempt  from  this  rule. 

When  part  of  one  member  is  detailed  the  same  as  another  member,  figures 
for  rivet  spacing  need  not  be  repeated;  refer  to  previous  sheet  or  sheets,  bearing 
in  mind  that  these  must  contain  final  information.  It  is  not  permissible  to 
refer  to  a  sheet,  which  in  turn  refers  to  another  sheet.  The  section,  finished 
length,  and  the  assembling  mark  for  each  member  shall  be  shown  on  every 
sheet.  Main  dimensions  which  are  necessary  for  checking,  such  as  c.  to  c. 
distances,  story  heights,  etc.,  shall  be  repeated  from  sheet  to  sheet.  Holes  for 
field  connections  must  always  be  located  independently,  even  if  figured  in 
connection  with  shop  rivets;  they  shall  be  repeated  from  sheet  to  sheet  unless 
they  are  standard,  in  which  case  they  shall  be  identified  by  a  mark  and  the  sheet 
given  on  which  they  are  detailed. 

The  quality  of  material,  workmanship,  size  of  rivets,  etc.,  shall  be  specified 
on  every  sheet  as  far  as  it  refers  to  the  sheet  itself.  Standard  workmanship 
need  not  be  specified  on  each  sheet. 


STRUCTURAL    DRAWINGS.  9 

Lettering. — Engineering  News  lettering  as  developed  by  Reinhardt  in  his 
book  on  freehand  lettering  shall  be  used  on  all  drawings.  Preferably  main 
titles  and  sub-titles  shall  be  vertical  and  the  remainder  of  the  lettering  inclined. 
The  height  of  letters  shall  be  as  follows:  Main  titles — capitals  15/50",  small 
capitals  12/50";  sub-titles — capitals,  full  height  lower  case  letters  and  numerals 
5/20",  lower  case  letters  3/20";  other  lettering — capitals,  full  height  lower  case 
letters  and  numerals  5/30",  lower  case  letters  3/30".  Where  the  drawing  is 
crowded  the  body  of  the  lettering  may  be  5/40"  and  3/40"  respectively.  The 
following  pens  are  recommended:  For  titles  Leonardt  &  Co.'s  Ball- Pointed 

TOP  CHOJZDS/* END  POSTS 
150 FOOT  Tfieouen  £fi/Lgof)D  BRIDGE 

0&E60N#fl/LWAYfNfiV/6ffr/ON  Co. 
POQTLAMD,  OGE. 

CO. 

Ch/Cf)6O,lLL. 

Chief  Engineer  AM$XBricfge  fa 

Drawn  by.     - AM  Johns tw- DaJbs....3-25-QQ... 

Checkedfy ZCfu/Jcr.. £*fe....j3L-2Zr.aa..- 

Order  No. &-Z82. Drawing-  No.....d358. 

Sheet.. _<4—.  of. —15. 

Approved..  CJC,  C,.Jc^u^i^rr. .  Cons  (//tin?  Eng/neer 


Cat  B/ue  Print  0/7  this  fine 


34" 


-K! 


II- 


Cat  Tracing  on  this  fine 


FIG.  6.     STANDARD  SHEET  AND  TITLE  FOR  STRUCTURAL  DRAWINGS. 


No.  5i6F;  for  all  other  lettering  Hunt  Pen  Co.'s  extra  fine  Shot  Point,  No. 
512.  No  pen  finer  than  Gillott's  No.  303  should  be  used.  Light  pencil  guide 
lines  shall  be  drawn  for  all  lettering.  All  tracings  shall  be  made  on  the  dull 
side  of  the  tracing  cloth.  Erasures  shall  be  made  with  soft  rubber  pencil 
eraser  and  a  metal  shield.  Rubber  erasers  containing  sand  destroy  the  surface 
of  the  cloth  and  make  it  difficult  to  ink  over  the  erased  spot.  The  use  of  knives 
or  stlel  erasers  will  not  be  permitted.  Tracings  shall  be  cleaned  with  a  very 
soft  rubber  eraser,  and  not  with  gasolene  or  benzine,  which  destroy  the  finish 
of  the  tracing  cloth.  All  lines  shall  preferably  be  made  with  black  India  ink; 
full  lines  to  represent  members,  dash  and  dot  to  represent  center  lines,  and 
dotted  lines  (or  full  light  black  lines)  to  represent  dimension  lines.  If  permitted 


10 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


STRUCTURAL    DRAWINGS. 


II 


12 


STRUCTURAL   DRAWINGS,   ESTIMATES   AND   DESIGNS. 


STRUCTURAL    DRAWINGS. 


by  the  chief  draftsman  red  ink  may  be  used  for  dimension  and  center  lines. 
The  ends  of  dimension  lines  shall,  however,  always  be  indicated  by  arrows 
made  with  black  ink. 

Conventional  Signs.    Conventional  signs  for  rivets  are  shown  in  Fig.  10. 
Countersunk  rivets  project  ^  in.;  if  less  height  of  rivets  is  required,  drawings 


Frefd  RirtfS 

A 


5hop  RJnfs 


Countersunk 

and 
Chip 


A  r 


it  it 


Countersunk 

and 
Chipped 


I  "i,VlS  ^ 
*  *MH8i, 

^-  ^ 


^  Pi 
O 


v*x  \~/ 


ffaffenect  fo £*  r  fattened '  fo  £"  Countersunk  but 

hiffh*  For^'l  high.  For  £"  Noi  Ghfppect  ^ 

•o  ancf  I " Rfvefs  and  £  "ft/vets  Wax*  Heiaht  o        5 


% 

5    O    ^S 

0 

iio 

_                                          J  

33 


FIG.  10.    CONVENTIONAL  SIGNS  FOR  RIVETS. 


14  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

shall  specify  that  they  are  to  be  chipped,  or  the  maximum  projection  may  be 
specified.  Flattened  heads  project  $i  in.  to  7/16  in.;  if  less  height  of  heads  is 
required,  they  shall  be  countersunk.  Metals  in  section  shall  be  shown  as  in 
Fig.  ii. 

Marking  System. — A  shipping  mark  shall  be  given  to  each  member  in  the 
structure,  and  no  dissimilar  pieces  shall  have  the  same  mark.  The  marks  shall 
consist  of  capital  letters  and  numerals,  or  numerals  only;  no  small  letters  shall 
be  used  except  when  sub-marking  becomes  absolutely  necessary.  The  letters 
R  and  L  shall  be  used  only  to  designate  "  right "  and  "  left."  Never  use  the 
word  "marked"  in  abbreviated  form  in  front  of  the  letter,  for  example  say, 
3  Floorbeams  G4,  and  not,  3  Floorbeams,  Mk.  G4.  Whenever  a  structure  is 
divided  up  into  different  contracts  care  should  be  taken  not  to  duplicate  ship- 


5teel         Cast  Iron       Cash  Steel         Bronze 
FIG.  ii.    CONVENTIONAL  SIGNS  FOR  METALS. 


ping  marks.  Pieces  which  are  to  be  shipped  bolted  on  a  member  shall  also 
have  a  separate  mark,  in  order  to  identify  them  should  they  for  some  reason  or 
another  become  detached  from  the  main  member.  The  plans  shall  specify  which 
pieces  are  to  be  bolted  on  for  shipment,  and  the  necessary  bolts  shall  be  billed. 
For  standard  marking  system  for  a  truss  bridge,  see  Fig.  7. 

A  system  of  assembling  marks  shall  be  established  for  all  small  pieces  in  a 
structure  which  repeat  themselves  -in  great  numbers.  These  marks  shall  con- 
sist of  small  letters  and  numerals  or  numerals  only;  no  capital  letters  shall  be 
used;  avoid  prime  and  sub-marks,  such  as  Ma.  Pieces  that  have  the  same 
assembling  mark  must  be  alike  in  every  respect;  same  section,  length,  cutting 
and  punching,  etc. 

Shop  Bills.  —  Shop  bills  shall  be  written  on  special  forms  provided  for  the 
purpose.  When  the  bills  appear  on  the  drawings  as  well,  they  shall  either  be 
placed  close  to  the  member  to  which  they  belong  or  on  the  right  hand  side  of 
the  sheet.  When  the  drawings  do  not  contain  any  shop  bills,  these  shall  be  so 
written  that  each  sheet  can  have  its  bill  attached  to  it  if  desired;  one  page  of 
shop  bills  shall  not  contain  bills  for  two  sheets  of  drawings.  In  large  structures 
which  are  sub-divided  into  shipments  of  suitable  size,  both  mill  and  shop  bills 
must  be  written  separately  for  each  shipment.  In  writing  the  shop  bill  bear  in 
mind  that  it  shall  serve  as  a  guide  for  the  laying  out  and  assembling  of  the 
member,  besides  being  a  list  of  the  material  required.  For  this  reason  members 
which  are  radically  different  as  to  material  shall  not  be  bunched  in  the  same 
shop  bill,  neither  shall  pieces  which  have  different  marks  be  bunched  in  the 
same  item,  even  if  the  material  is  the  same.  Bill  first  the  main  material  in  the 
member,  and  follow  with  the  smaller  pieces,  beginning  at  the  left  end  of  a 


STRUCTURAL    DRAWINGS.  I  5 

girder,  or  at  the  bottom  of  a  post  or  girder.  On  a  column  each  different 
bracket  shall  be  billed  complete  by  itself.  Do  not  bill  first  all  the  angles  and 
then  all  the  flats ;  for  example  when  the  end  stiffeners  in  a  girder  are  billed, 
the  fillers  belonging  to  them  shall  follow  immediately  after  the  angles,  and  so  on. 
When  machine-finished  surfaces  are  required,  the  drawing  and  the  shop 
bill  shall  specify  the  finished  width  and  length  of  the  piece,  the  proper  allowance 
for  shearing  and  planing  being  made  in  the  mill  bill.  When  the  metal  is  to  be 
planed  as  to  thickness,  the  drawing  and  the  shop  bill  shall  specify  both  the 
ordered  and  the  finished  thickness ;  one  pi.  15"  X  ^"  X  i'  6"  (planed  from 

13/16")- 

Field  bolts  shall  be  billed  on  "bill  of  rivets  and  bolts"  only.  Bill  them 
Similarly  to  field  rivets,  and  give  the  drawing  number  on  which  they  are  shown; 
4— bolts  7/8"  X  2"  grip,  3"  U.K.,  stringers  "  S  "  to  floor  beam  "  F  "  drawing  No. 
13,  4  hex.  (or  4  square)  nuts  for  above  bolts.  Bill  of  bolts  and  bill  of  field 
rivets  shall  be  prepared  and  placed  in  the  shop  in  time  to  be  made  with  other 
material. 

Erection  Plan. — Make  erection  plans  simultaneously  with  the  shop  plans, 
and  keep  same  up  to  date.  The  erection  plans  must  show  plainly  the  style  of 
connections;  joints  in  pin  spans  are  to  be  shown  separately  to  a  larger  scale. 
For  the  erection  plan  of  a  truss  bridge  see  Fig.  7.  Shipping  bills  showing  the 
number  of  pieces,  erection  mark,  and  weight  shall  be  made  for  each  shipment. 

Sub-Divisions. — Every  contract  embracing  different  classes  of  work  shall 
have  a  subdivision  for  each  class.  These  sub-divisions  will  be  furnished  by  the 
chief  draftsman.  Drawings,  shop  and  shipping  bills  must  be  kept  separate  for 
each  class. 

PLATE  GIRDER  BRIDGES.— General  Rules.— The  plate  girder  span 
shall  be  laid  out  with  regard  to  the  location  of  web  splices,  stiffeners,  cover 
plates,  and  in  a  through  span,  floorbeams  and  stringers,  so  that  the  material 
can  be  ordered  at  once.  Locate  splices  and  stiffeners  with  a  view  of  keeping 
the  rivet  spacing  as  regular  as  possible ;  put  small  fractions  at  the  end  of  girder. 
Stiffeners,  to  which  cross-frames  or  floorbeams  connect,  must  not  be  crimped, 
but  shall  always  have  fillers.  The  outstanding  leg  shall  not  be  less  than  4", 
gaged  2^";  this  will  enable  cross-frames  or  floorbeams  to  be  swung  in  place 
without  spreading  the  girders.  The  second  pair  of  stiffeners  at  the  end  of 
girder  over  the  bed-plate  shall  be  placed  so  that  the  plate  will  project  not  less 
than  i"  beyond  the  stiffeners. 

Always  endeavor  to  use  as  few  sizes  as  possible  for  stiffeners,  connection 
plates,  etc.,  and  avoid  all  unnecessary  cutting  of  plates  and  angles.  For  this 
purpose  locate  end  holes  for  laterals  and  diagonals  so  that  the  members  can  be 
sheared  in  a  single  operation.  In  spans  on  a  grade,  unless  otherwise  specified, 
put  the  necessary  bevel  in  the  bed-plate  and  not  in  the  base-plate.  In  short 
spans,  say  up  to  50  feet,  put  slotted  holes  for  anchor-bolts  in  both  ends  of 
girders,  Y%'  larger  diameter  than  the  anchor  bolts. 

In  square  spans,  show  only  one-half,  but  give  all  main  dimensions  for  the 
whole  span.  In  skew  spans  show  the  whole  span;  when  the  panels  in  one-half 


1 6  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

of  span  are  same  as  in  the  other  half,  give  the  lengths  of  these  panels,  but  do 
not  repeat  rivet-spacing,  except  where  it  differs. 

In  the  small  scale  diagram,  which  shall  appear  on  every  sheet,  unless  span 
is  drawn  in  full,  show  the  position  of  stiffeners,  particularly  those  to  which 
cross-frames  or  floorbeams  connect. 

Deck  Plate  Girder  Spans.— On  top  of  sheet  show  a  top  view  of  span,  with 
cross-frames,  laterals  and  their  connections  complete,  with  the  girders  placed  at 
right  distances  apart.  Below  this  view  show  the  elevation  of  the  far  girder  as 
seen  from  the  inside,  with  all  field  holes  in  flanges  and  stiffeners  indicated  and 
blackened.  At  one  end  of  the  elevation  show  in  red  the  bridge-seat  and  back 
wall,  give  figures  for  distance  from  base  of  rail  to  top  of  masonry,  notch  of 
ties,  depth  of  girder,  thickness  of  base-plate  and  of  bed-plate  or  shoe.  When 
the  other  end  of  girder  has  a  different  height  from  base  of  rail  to  masonry, 
give  both  figures  at  the  one  end,  and  specify  "  for  this  end "  and  "  for  other 
end."  If  span  has  bottom  lateral  bracing,  a  bottom  view  (horizontal  section) 
shall  be  shown  below  the  elevation.  When  no  bottom  laterals  are  required, 
show  only  end  or  ends  of  lower  flange  of  girder,  giving  detail  of  base-plate  and 
its  connection  to  the  flange.  Detail  the  bed-plate  separately,  never  show  it  in 
connection  with  the  base-plate. 

Cross-frames  shall,  whenever  possible,  be  detailed  on  the  right  hand  of  the 
sheet  in  line  with  the  elevation.  The  frame  shall  be  made  of  such  depth  as  to 
permit  it  being  swung  into  place  without  interfering  with  the  heads  of  the 
flange  rivets  in  the  girders.  Always  use  a  plate,  not  a  washer  with  one  rivet, 
at  the  intersection  of  diagonals.  In  skew  spans  it  is  always  preferable  to  have 
an  uneven  number  of  panels  in  the  lateral  system. 

Through  Plate  Girder  Spans. — Show  on  top  of  sheet  an  elevation  of  the 
far  girder  as  seen  from  inside;  below  this  view  show  a  horizontal  section  of 
span  as  seen  from  above  with  the  lateral  system  detailed  complete.  It  is  gen- 
erally best  to  show  floorbeams  and  stringers  in  red  in  this  view  and  to  detail 
them  on  a  separate  sheet.  The  stiffeners  in  a  through  span  should  always  be 
arranged  so  that  the  floor  system  can  be  put  in  place  from  the  center  towards 
the  ends.  What  is  said  under  "  deck  spans "  about  showing  bridge-seat,  back 
wall,  detailing  bed-plate  separately,  etc.,  applies  to  through  spans  as  well. 

TRUSS  BRIDGES. — General  Rules.— Before  any  details  are  started  all 
c.  to  c.  lengths  of  chords,  posts,  diagonals,  etc.,  shall  be  determined,  and  sketches 
made  of  shoes,  panel-points,  splices,  etc.,  so  that  the  material  can  be  ordered  as 
soon  as  required. 

If  not  otherwise  specified,  camber  shall  be  provided  in  the  top  chord  by 
increasing  the  length  l/%"  for  every  10  feet  for  railroad  bridges,  and  3/16"  for 
every  10  feet  for  highway  bridges.  This  increase  in  length  shall  not  be  con- 
sidered in  figuring  the  length  of  the  diagonals,  except  in  special  cases,  as 
directed  by  the  engineer  in  charge.  Half  the  increase  in  length  shall  be  con- 
sidered in  figuring  the  length  of  the  top  laterals.  Particular  attention  must  be 
paid  to  what  is  said  under  "General  Rules"  about  showing  part  of  adjoining 
member  in  red,  and  about  the  small  scale  diagram  on  every  sheet. 


STRUCTURAL    DRAWINGS.  I/ 

For  every  truss  bridge  an  erection  diagram  shall  be  made  on  a  separate 
sheet,  giving  the  shipping  marks  of  the  different  members  and  all  main  dimen- 
sions, such  as  c.  to  c.  trusses,  height  of  truss,  number  and  length  of  panels, 
length  of  diagonals,  distance  from  base  of  rail  to  masonry,  distance  from  center 
of  bottom  chord  or  pin  to  masonry,  size  and  grip  of  pins  (Fig.  7),  also  show  in 
larger  scale  the  packing  at  panel  points,  state  any  special  feature  which  the 
erector  needs  to  look  out  for,  and  give  approximate  weight  of  heavy  and 
important  pieces  when  their  weight  exceeds  five  tons.  If  in  any  place  it  is  doubt- 
ful whether  rivets  can  be  driven  in  the  field,  the  erection  diagram  and  also  the 
detail  drawings  shall  state  that  "turned  bolts  may  be  used  if  rivets  cannot  be 
driven."  A  list  giving  number  and  contents  of  drawings  belonging  to  the  bridge 
shall  also  appear  on  the  erection  diagram  sheet. 

Riveted  Truss  Bridges. — In  square  spans,  not  too  large,  show  the  left  half 
of  the  far  truss  as  seen  from  the  inside  and  detail  all  members  in  their  true 
position,  making  scale  of  the  skeleton  one-half  the  scale  of  the  details.  In  skew 
spans,  not  symmetrical,  show  the  whole  of  the  far  truss.  In  large  spans  detail 
every  member  separately.  When  detailing  web  members  bear  in  mind  that  the 
intersection  point  on  the  chord  must  not  be  used  as  a  working  point  for  a 
member  which  stops  outside  of  the  chord.  A  separate  working  point,  prefer- 
ably the  end  rivet,  shall  be  established  on  the  member  proper,  and  shall  be  tied 
up  with  the  intersection  point  on  the  chord. 

The  clearance  between  the  chord  and  a  web  member  entering  same  shall, 
whenever  possible,  be  not  less  than  y%"  in  heavy  and  1/16"  in  light  structures. 

Members  shall  be  marked  with  the  panel  points  between  which  they  go,  for 
example,  end  post  Lo~Ui;  hip  vertical  Ui-Li;  top  chord  Ui-Uz,  etc.,  see  Fig.  7. 

Pin-connected  Truss  Bridges. — In  pin-connected  truss  bridges  detail  the 
left  half  of  the  far  truss  as  seen  from  the  inside,  every  member  by  itself.  It  is 
generally  best  to  commence  with  the  end  post,  showing  it  lengthwise  on  the 
sheet  with  the  lower  end  to  the  left;  then  the  first  section  of  the  top  chord,  and 
so  on.  The  packing  at  panel  points  shall,  whenever  possible,  be  so  arranged 
that,  besides  the  customary  allowance  of  1/16"  for  every  bar,  a  clearance  of  not 
less  than  ^"  can  be  provided  between  the  two  sides  of  the  chord.  When  two 
or  more  plates  are  used,  1/32"  should  in  addition  be  allowed  for  each  plate. 
Members  shall  be  marked  the  same  as  for  riveted  truss  bridges,  with  the  panel 
points  between  which  they  go,  see  Fig.  7. 

Order  of  Detailing  Truss  Spans. — In  making  detail  plans  and  bills  of 
material  the  following  order  shall  be  followed  for  truss  spans. 

1.  General  Drawing; 

2.  End  posts; 

3.  Upper  chords; 

4.  Lower  chords; 

5.  Intermediate  posts; 

6.  Sway  bracing; 

7.  Upper  laterals; 

8.  Lower  laterals; 


i8 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


9.  Floorbeams; 

10.  Stringers; 

11.  Castings,  bolts,  eye-bars,  pins,  etc. 

OFFICE  BUILDINGS  AND  STEEL  FRAME  BUILDINGS.— Num- 
ber of  Drawings. — The  different  sheets  shall  be  numbered  consecutively,  whether 
large  or  small.  No  half  numbers  are  permissible  except  in  emergency  cases. 
It  is  always  well  to  arrange  the  number  so  that  the  sheets  follow  in  the  order 


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STRUCTURAL    DRAWINGS.  1 9 

in  which  the  material  is  required  at  the  building.    The  following  is  generally  a 
good  order: 

1.  Floor  plans  for  all  floors; 

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FIG.  13.    COLUMN   SCHEDULE  FOR  OFFICE  BUILDINGS. 

4.  Foundation  girders; 

5.  Foundation  beams; 

6.  First  tier  of  columns; 

7.  Riveted  girders,  connecting  to  first  tier  of  columns; 

8.  Beams  connecting  to  first  tier  of  columns; 


2O  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

9.  Miscellaneous  material  for  above; 
10.  Second  tier  of  columns,  etc.,  etc. 

Floor  Plans. — Floor  plans,  Fig.  12,  shall,  as  a  rule,  be  made  to  a  scale  W 
to  i  ft.  A  separate  plan  shall  be  made  for  each  floor,  unless  they  are  exactly 
alike.  Columns  shall  be  marked  consecutively  with  numerals,  the  word  Col. 
always  appearing  in  front  of  the  numeral,  for  example,  Col.  20.  The  archi- 
tect or  engineer  has  generally  on  his  drawing  adopted  a  system  of  marking 
for  the  columns,  which  should  be  adhered  to,  unless  altogether  too  imprac- 
ticable. Riveted  girders  shall  be  indicated  with  two  (2)  fine  lines  when  they 
have  cover  plates,  and  with  four  (4)  fine  lines  when  they  have  no  cover  plates. 
They  shall  be  marked  consecutively  with  numerals,  using  the  same  marks  for 
girders  which  are  alike.  Beams  and  channels  shall  be  indicated  with  one  single 
heavy  line.  They  shall  be  marked  the  same  as  girders,  with  numerals,  using 
same  marks  when  alike.  Tie-rods  shall  be  indicated  with  one  single  fine  line; 
they  need  not  have  any  marks.  The  marking  system  shall  be  as  uniform  as 
possible  for  the  different  floors,  i.  e.,  a  beam  which  goes  between  Col.  2  and 
Col.  3  shall  be  marked  with  the  same  numeral  throughout  all  the  floors.  All 
figures  necessary  for  making  the  details  shall,  as  a  rule,  appear  on  the  floor 
plan,  care  being  taken  in  writing  same  to  leave  room  for  the  erection  marks, 
which  must  be  printed  in  heavy  type  above  the  line  or  lines  representing  a 
beam  or  girder. 

Column  Schedule. — For  a  very  large  building  a  schedule  of  the  columns 
shall  be  made  before  the  details  are  started,  see  Fig.  13.  Each  column,  even 
should  several  be  alike,  shall  have  a  separate  space,  in  which  shall  be  given  the 
material  and  the  finished  length.  As  soon  as  the  detail  drawings  for  one  tier  of 
columns  are  finished  the  sheet  numbers  shall  be  inserted  as  shown  on  the  sample 
schedule,  Fig.  13,  making  the  schedule  serve  as  an  index  for  the  column 
drawings. 

Columns. — Columns  shall,  whenever  possible,  be  drawn  standing  up  on  the 
sheets  as  they  appear  in  the  building.  If  it  becomes  necessary  to  draw  them 
lengthwise  on  the  sheet,  the  base  shall  be  to  the  left.  Particular  attention  shall 
be  paid  to  establishing  a  marking  system  for  brackets,  splice-plates,  etc.  A 
summary  of  all  these  standard  pieces  shall  be  made  for  each  tier  and  sent  to 
the  shop  as  early  as  practicable,  in  order  that  they  may  be  gotten  out  before  the 
main  material  is  taken  up.  The  material  for  the  small  pieces  shall,  as  far  as 
possible,  be  chosen  from  stock  sizes.  Columns  shall  be  marked  with  the  num- 
ber of  the  floor  between  which  they  go;  Col.  5  (1-3).  The  lower  tier  is  best 
marked  "Basement  Tier."  Standard  details  for  columns  are  given  in  Fig.  14 
and  Fig.  15. 

Riveted  Girders. — Girders  shall  be  marked  with  the  number  of  the  floors, 
not  with  letters,  unless  requested;  for  example,  2d  Floor,  No.  5.  What  is  said 
under  columns  about  marking  system  for  standard  pieces  applies  to  girders  as 
well.  When  a  girder  is  unsymmetrical  about  the  center  line,  and  a  question 
may  arise  how  to  erect  it,  one  end  shall  be  marked  with  the  number  of  the 
column  to  which  it  connects,  or  with  North,  South,  East  or  West.  Girders 


STRUCTURAL    DRAWINGS. 


21 


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FIG.  14.     STANDARD  DETAILS   FOR   BETHLEHEM    H-COLUMNS. 


must  not  be  bunched  together  for  the  different  floors  more  than  to  meet  the 
requirements  in  the  field;  but  they  must  correspond  to  the  tiers  of  columns  as 
they  will  be  erected. 


22 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


STRUCTURAL    DRAWINGS. 


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FIG.  16.    STANDARD  DETAILS  FOR  ROLLED  BEAMS. 


24  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

Beams. — Beams  shall  be  drawn  on  the  standard  forms  provided  for  the 
purpose.  They  need  not  be  drawn  to  scale,  see  Fig.  16  and  Fig.  17.  Beams 
shall  be  marked  the  same  as  girders  with  the  number  of  the  floor;  One  12"  I  @ 
40  Ibs.  X  i9'-3^",  (Mark)  2d  Floor  No.  35.  What  is  said  under  girders  about 
marking  one  end,  when  not  symmetrical  around  the  center  line,  and  about  not 


1 6irder-5?l-3rdFI. 


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FIG.  17.    STANDARD  DETAILS  FOR  ROLLED  BEAMS. 


bunching  the  different  floors  more  than  to  meet  the  requirements  in  the  field, 
applies  to  beams  as  well. 

Whenever  possible  use  standard  framing  angles,  Tables  7  and  8.  If  it  is 
deemed  necessary  to  use  6"  X  6"  angles,  punch  both  legs  the  same  as  the  6"  leg 
of  standard;  in  3^"  X  3^"  or  4"  X  3^"  angles,  punch  both  legs  the  same  as 
4"  leg  of  standard.  It  is  not  absolutely  imperative  that  the  gage  of  the  framing 
angles  shall  be  standard  as  long  as  the  vertical  distance  between  the  holes  and 
in  the  6"  leg  the  horizontal  distance  (2^"),  are  kept  standard.  Holes  for 
connections,  tie-rods,  etc.,  shall  be  located  from  one  end  of  the  beam,  preferably 


STRUCTURAL    DRAWINGS.  25 

the  left.  If  one  end  rests  on  the  wall  and  the  other  end  is  framed,  then  figure 
from  the  latter  end,  be  it  right  or  left.  This  rule  may  be  dispensed  with  in 
case  of  numerous  holes  regularly  spaced  in  web  or  flange  for  connection  of 
shelf-angles,  buckle-plates,  etc.  The  allowed  overrun  at  ends  of  beams  must 
always  be  indicated,  either  by  giving  figures  or  by  showing  wall  bearing.  Holes 
at  the  end  of  beam  for  anchors  are  best  figured  from  wall  end,  not  connecting 
them  with  other  figures.  The  distance  between  end  holes  in  beams  which  con- 
nect through  web  or  flange  to  columns,  girders,  etc.,  .shall  always  be  given. 
When  framing  angles  are  standard,  do  not  give  any  figures  for  either  shop  or 
field  rivets,  except  the  distance  from  bottom  of  beam  to  center  of  connection 
or  to  first  holes  in  framing  angle,  and  the  horizontal  distance  between  field 
holes.  When  special  framing  angles  are  used,  the  fact  must  be  noted  and  figures 
given  for  gages,  etc.  For  standard  connection  holes  in  web  of  beam  all  figures 
required  are  the  distance  from  bottom  of  beam  to  centre  of  connection  or  to 
first  hole  and  the  horizontal  distance  between  holes.  Whenever  possible  use 
standard  punching. 

ERECTION  PLAN  FOR  MILL  BUILDINGS.— The  preceding  method 
for  office  buildings  will  need  considerable  modification  for  steel  frame  mill 
buildings.  The  following  method  for  making  erection  plans  for  steel  frame 
mill  buildings  has  been  found  very  satisfactory. 

If  the  points  of  the  compass  are  known,  mark  all  pieces  on  the  north  side 
with  the  letter,  N,  those  on  the  south  with  the  letter,  S,  etc.  Mark  girts  N.G.I  ; 
N.G.2;  etc.  Mark  all  posts  with  a  different  number,  thus:  N.P.i;  N.P.2;  etc. 
Mark  small  pieces  which  are  alike  with  the  same  mark;  this  would  usually 
include  everything  except  posts,  trusses  and  girders,  but  in  order  to  follow  the 
general  marking  scheme,  where  pieces  are  alike  on  both  sides  of  a  building,  change 
the  general  letter;  e.  g.,  N.G.7  would  be  a  girt  on  the  north  side  and  S.G.7  the 
same  girt  on  south  side.  Then  in  case  the  north  and  south  sides  are  alike,  only 
an  elevation  of  one  side  need  be  shown,  and  under  it  a  note  thus :  "  Pieces  on 
south  side  of  building,  in  corresponding  positions  have  the  same  number  as  on 
this  side,  but  prefixed  by  the  letter,  S,  instead  of  the  letter,  N."  Mark  trusses 
T.I;  T.2;  etc.  Mark  purlins  R.I;  R.2;  etc. 

The  above  scheme  will  necessarily  have  to  be  modified  more  or  less  accord- 
ing to  circumstances ;  for  example,  where  a  building  has  different  sections  or 
divisions  applying  on  the  same  order  number,  in  which  case  each  section  or 
division  should  have  a  distinguishing  letter  which  should  prefix  the  mark  of 
every  piece.  In  such  cases  it  will  perhaps  be  well  to  omit  other  letters,  such  as 
N.,  S.,  etc.,  so  that  the  mark  will  not  be  too  long  for  easy  marking  on  the  piece. 
In  general,  however,  the  scheme  should  be  followed  of  marking  all  the  larger 
pieces,  whether  alike  or  not,  with  a  different  mark.  This  would  refer  to  pieces 
which  are  liable  to  be  hauled  immediately  to  their  places  from  the  cars.  But 
for  all  smaller  pieces  which  are  alike,  give  the  same  mark. 

DETAIL  NOTES. — Sections. — End  views  of  sections  shall  be  shown  as 
in  (a)  Fig.  18,  and  sections  shall  be  cross-hatched  or  blackened  as  shown  in 
(b)  Fig.  18. 


26 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


Assembling  Note.— Covers,  webs,  flange  angles,  etc.,  must  not  be  marked 
alike  when  it  would  be  necessary  to  turn  them  end  for  end,  see  (c)  Fig.  18. 

Rivet  Spacing. — Rivet  spacing  must  be  tied  up  from  end  to  end. 

Connection  Plates. — In  detailing  connection  plates  wherever  bevel  for 
holes  on  lines  "  b,"  (d)  and  (e)  Fig.  18,  is  different,  spacing  for  holes  on  lines 
"a"  should  be  made  different  to  prevent  plates  from  being  interchanged. 


3ZI 


(a; 


(b) 


4 


-f 


r~r'T~~i 

r4—  i  "—  h 

<y          1 

r<yy" 

-M-t-+- 

+  >> 
r     7>. 

-_^^-»-t- 

•  -^w 

^-  2-i 

i          * 

N 

1 

V-^ 

*i  X 

i 

-^ 


(C) 


(d) 


"12" 


12' 


(e) 


FIG.  18. 


Writing  Angles.  —  In  writing  angles  give  the  longer  leg  first,   i-L  6"  X 
4"  X  y2"  X 


Writing  Plates.  —  In  writing  plates  the  width  of  the  plate  is  given  in  inches, 
the  thickness  in  inches,  and  the  length  in  feet  and  inches  ;  2-P1.  48"  X  W  X  15'- 
0^4".  A  length  of  9  inches  should  be  written  o'-o/'.  and  not  9".  The  width  of  a 
plate  is  the  dimension  at  right  angles  to  the  length  of  the  member,  while  the 
length  of  a  plate  is  the  dimension  parallel  to  the  length  of  the  member  to  which 
the  plate  is  attached  ;  except  that  for  lacing  bars,  tie  plates  and  other  universal 
mill  plates  6  inches  and  less  in  width  the  least  dimension  is  taken  as  the  width 
of  the  member,  and  for  splice  plates  the  width  is  the  dimension  at  right  angles 
to  the  splice. 

Writing  Sections.—  Sections  are  written  as  follows:  i-I  12"  (a)  40  Ibs.  X 


Miscellaneous.  —  Bevels  may  be  shown  as  so  many  inches  in  12",  (a)  Fig.  19; 
or  where  convenient  the  total  lengths  may  be  given  as  in  (b)  Fig.  19.  The  latter 
method  is  the  better  as  it  assists  the  checker  and  the  templet  maker. 

The  maximum  amount  that  one  leg  of  an  angle  can  be  bent  is  45°.  For  a 
greater  bend  than  45°  a  bent  plate  shall  be  used,  (c)  Fig.  19. 

The  center  to  center  length  of  stiff  laterals  should  be  not  less  than  1/16" 
short. 

Do  not  use  2  sizes  of  rivets  in  the  same  leg,  or  same  angle,  or  same  piece 
unless  absolutely  necessary. 


STRUCTURAL    DRAWINGS.  2/ 

Where  unequal  legged  angles  are  used  mark  the  width  of  one  leg  of  the 
angle  on  the  leg. 

Where  heavy  laterals  are  spliced  in  the  middle  by  a  plate,  ship  the  plate 
riveted  to  one  angle  only. 

Do  not  countersink  rivets  in  long  pieces  unless  absolutely  necessary. 

Do  not  draw  any  more  of  a  member  than  necessary,  and  do  not  dimension 
the  same  piece  several  times. 

Revising  Drawings. — When  drawings  have  been  changed  after  having  been 
first  approved,  they  must  be  marked,  Revised  (give  date  of  revision). 


FIG.  19. 

Measuring  Angles. — All  measurements  on  angles  are  to  be  made  from  the 
back  of  the  angle,  and  not  from  the  edge  of  the  flange.  The  center  to  center 
distance  between  open  holes  should  always  be  given  for  each  piece  that  is 
shipped  separate,  in  order  that  the  inspector  can  check  the  piece. 

Width  of  Angles.— The  widths  of  the  legs  of  angles  are  greater  than  the 
nominal  widths,  unless  the  angle  has  been  rolled  with  a  finishing  roll.  The 
over-run  for  each  leg  is  equal  to  the  nominal  width  of  the  leg  plus  the  increase 
in  thickness  of  leg  made  by  spreading  the  rolls.  For  example  finishing  rolls  are 
used  for  rolling  3"  X  3"  angles  with  a  thickness  of  y±" .  The  actual  length  of 
the  leg  of  a  3"  X  3"  angle  is  as  follows:  angle  3"  X  3"  X  $4",  leg  3";  angle 
3"  X  3"  X  5/16",  leg  3  1/16";  angle  3"X  3"  X  ft",  leg  3^";  angle  3"  X  3"  X  y2" , 
leg  3J4"J  angle  3"  X  3"  X  ft",  leg  33/s"- 

POINTS  TO  BE  OBSERVED  IN  ORDER  TO  FACILITATE 
ERECTION. — The  first  consideration  for  ease  and  safety  in  erection  should 
be  to  so  arrange  all  details,  joints  and  connections  that  the  structure  may  be 
connected  and  made  self-sustaining  and  safe  in  the  shortest  time  possible. 
Entering  connections  of  any  character  should  be  avoided  when  possible, 
notably  on  top  chords,  floor  beam  and  stringer  connections,  splices  in  girders, 
etc.  When  practicable,  joints  should  be  so  arranged  as  to  avoid  having  to  put 
members  together  by  entering  them  on  end,  as  it  is  often  impossible  to  get  the 
necessary  clearance  in  which  to  do  this.  In  all  through  spans  floor  connections 
should  be  so  arranged  that  the  floor  system  can  be  put  in  place  after  the  trusses 
or  girders  have  been  erected  in  their  final  position,  and  vice  versa,  so  that  the 


28  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

trusses  or  girders  can  be  erected  after  the  floor  system  has  been  set  in  place. 
All  lateral  bracing,  hitch-plates,  rivets  in  laterals,  etc.,  should,  as  far  as  possible, 
be  kept  clear  of  the  bottoms  of  the  ties,  it  being  expensive  to  cut  out  ties  to 
clear  such  obstructions.  Lateral  plates  should  be  shipped  loose,  or  bolted  on 
so  that  they  do  not  project  outside  of  the  member,  whenever  there  is  danger  of 
their  being  broken  off  in  unloading  and  handling.  Loose  fillers  should  be 
avoided,  but  they  should  be  tacked  on  with  rivets,  countersunk  when  necessary. 

In  elevated  railroad  work,  viaducts  and  similar  structures,  where  longi- 
tudinal girders  frame  into  cross  girders,  shelf  angles  should  be  provided  on 
the  latter.  In  these  structures  the  expansion  joints  should  be  so  arranged  that 
the  rivets  connecting  the  fixed  span  to  the  cross  girder  can  be  driven  after  the 
expansion  span  is  in  place.  In  viaducts,  etc.,  two  spans,  abutting  on  a  bent, 
should  be  so  arranged  that  either  span  can  be  set  in  place  entirely  independent 
of  the  other.  The  same  thing  applies  to  girder  spans  of  different  depth  resting 
on  the  same  bent.  Holes  for  anchor-bolts  should  be  so  arranged  that  the  holes 
in  the  masonry  can  be  drilled  and  the  bolts  put  in  place  after  the  structure  has 
been  erected  complete. 

In  structures  consisting  of  more  than  one  span  a  separate  bed-plate  should 
be  provided  for  each  shoe.  This  is  particularly  important  where  an  old  struc- 
ture is  to  be  replaced;  if  two  shoes  were  put  on  one  bed  plate  or  two  spans 
connected  on  the  same  pin,  it  would  necessitate  removing  two  old  spans  in 
order  to  erect  one  new  one.  In  pin-connected  spans  the  section  of  top  chords 
nearest  the  center  should  be  made  with  at  least  two  pin-holes.  In  skew  spans 
the  chord  splices  should  be  so  located  that  two  opposite  panels  can  be  erected 
without  moving  the  traveler.  Tie  plates  should  be  kept  far  enough  away  from 
the  joints  and  enough  rivets  should  be  countersunk  inside  the  chord  to  allow 
eye-bars  and  other  members  being  easily  set  in  place.  Posts  with  channels  or 
angles  turned  out  and  notched  at  the  ends  should  be  avoided  whenever  possible. 

ORDERING  MATERIAL.— Bridge  Work.— Ordinarily  plates  less  than 
48"  wide  are  ordered  U.  M.  (universal  mill  or  edge  plates),  but  when  there  is 
no  need  for  milled  edges  and  prompt  delivery  is  essential  specify  either  U.  M. 
or  sheared.  Never  order  widths  in  eighths.  Flats  and  universal  (edge)  plates 
over  4"  in  width  should  be  ordered  in  even  inches,  flats  under  4"  should  be 
ordered  by  y2"  variation  in  width.  Flats  Y^"  and  under  in  thickness  are  very 
difficult  to  secure  from  the  mills  and  should  be  avoided  if  possible. 

Rolling  mills  are  allowed  a  variation  of  Y^"  in  width  of  plates,  over  or 
under,  and  a  variation  of  ^"  in  length,  over  or  under,  from  the  ordered  width 
or  length.  Rolling  mills  are  allowed  a  variation  of  ^"  over  or  under  the 
ordered  length  of  beams,  channels,  angles,  zees,  etc.  An  extra  price  is  charged 
for  cutting  to  exact  length. 

Allow  1/16"  in  thickness  for  planing  plates  2'  6"  square  or  less,  Y&"  f°r  plates 
more  than  2'  6"  square,  and  %"  for  columns;  chords  and  girders  which  have 
milled  ends  are  ordered  Y^"  longer  than  the  finished  dimensions. 

Web  plates  should  be  ordered  Yz"  less  than  the  back  to  back  of  flange 
angles  unless  a  less  clearance  is  specified.  Web  plates  should  preferably  be 
ordered  in  even  inches  and  the  distance  back  to  back  of  angles  made  in  fractions. 


STRUCTURAL    DRAWINGS.  2Q 

When  angles,  beams  or  channels  are  bent  in  a  circle  allow  9"  to  12"  for 
bending. 

Bent  plates  should  be  ordered  to  the  length  of  the  outside  of  the  bend. 

Large  gusset  plates,  large  plates  with  angle  cuts,  etc.,  should  be  ordered  as 
sketch  plates,  when  the  amount  of  waste  if  ordered  rectangular  will  exceed  20 
per  cent.  Mills  will  not  make  re-entrant  cuts  in  plates  or  shapes. 

In  ordering  lacing  bars  add  3/16"  to  the  finished  length  and  order  in  mul- 
tiple lengths. 

ORDERING  MATERIAL.— Building  Work.— Order  beams  in  founda- 
tion neat  length. 

Order  beams  framing  into  beams  Y%'  short  for  each  end,  see  Fig.  20. 

Order  main  column  material  £4"  long  for  milling  both  ends  (this  takes  care 
of  permissible  variation  in  length  of  plus  or  minus  f£  in.  as  well  as  the  milling). 

Order  girder  flange  angles  and  plates  i"  long. 


Length  out_  to  ou_t 
FIG.  20.    BEAMS   BETWEEN   COLUMNS. 

Order  girder  web  plates  5/2"  short,  where  end  connections  are  used. 

Order  girder  web  plates  neat  length,  where  end  connections  are  not  used. 

Order  girder  web  plates  y2"  less  in  width  than  back  of  flange  angles. 

Order  stiffener  angles  %"  long. 

Order  fillers  under  stiffeners  neat  length. 

Add  3/16"  to  each  lacing  bar  and  order  in  multiple  lengths. 

SHAPES   AND   PLATES   MOST   EASILY    OBTAINED.— The   ease 

with  which  different  commercial  sizes  of  shapes  and  plates  may  be  obtained 
from  the  rolling  mill  varies  with  the  mill  and  with  the  demand.  Where  any 
section  is  in  demand  rollings  are  frequent  and  the  orders  are  promptly  filled, 
while  the  order  for  a  section  not  in  demand  may  have  to  wait  a  long  time  until 
sufficient  orders  have  accumulated  to  warrant  a  special  rolling. 

The  following  list  of  plates  and  sections  is  fairly  accurate,  the  list  varying 
from  time  to  time. 


34 


3<D  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

Plates. — Plates  most  easily  obtained. 


Width, 

1WOL       WClOll.^         »_/  U/t,CA,AA* 

Thickness, 

Width, 

Thickness, 

Ins. 

Ins. 

Ins. 

Ins. 

li 

:&  and  i 

5 

£  and  up 

ll 

&  and  i 

6 

•k  and  up 

2 

A  and  i 

7 

^  and  up 

2i 

i  and  up 

8 

I  and  up 

2i 

i  and  up 

9 

i  and  up 

3 

i  and  up 

10 

1  and  up 

34 

i  and  up 

12 

i  and  up 

4 

£  and  up 

14 

£  and  up 

Over  14"  in  width  it  is  immaterial  what  width  of  plate  is  specified. 

Squares  and  Rounds. — Squares  and  rounds  most  easily  obtained. 

Rounds,  5/s",  tt",  7/&",  i",  IJ4",  !#"• 

Squares,  ft",  ft",  i",  i#",  i%". 

All  other  sizes  are  liable  to  cause  delay. 

Beams. — Sizes  of  I-Beams  which  can  be  obtained  most  readily. 

Depth.  Weight. 

6"  I2i  Ibs. 

8"  18    Ibs.  2oi  Ibs. 

10"  25    Ibs.  30  Ibs. 

12"  314  Ibs.  35  Ibs.    40  Ibs. 

15"  42    Ibs.  50  Ibs.    60  Ibs. 

18"  55    Ibs.  60  Ibs.    70  Ibs. 

20"  65    Ibs.  80  Ibs. 

24"  80    Ibs.  90  Ibs.  100  Ibs. 

Sizes  of  I-Beams  which  may  be  used  but  for  which  prompt  deliveries  may 
not  be  expected. 

Depth.  Weight. 

5"  9!  Ibs. 

7"  15    Ibs. 

9"  21     Ibs.  25  Ibs. 

Beams  of  weights  different  from  the  above  can  always  be  obtained  from 
the  mills  but  not  so  readily  as  those  given.  Beams  of  minimum  section  can 
always  be  obtained  more  readily  than  heavier  sections. 

Channels.— Channels  which  can  be  most  readily  obtained  from  the  mills. 

Depth.  Weight. 

6"  8  Ibs. 

8"  ill  Ibs.  i8f  Ibs. 

10"  15  Ibs.  20  Ibs.  25  Ibs. 

12"  .         2oi  Ibs.  25  Ibs.  30  Ibs. 

15"  33  Ibs.  40  Ibs.  50  Ibs. 


STRUCTURAL    DRAWINGS.  31 

Sizes  which  may  be  used  but  for  which  prompt  deliveries  cannot  be  ex- 
pected. 

Depth.  Weight. 

5"  6i  Ibs. 

f  9*  Ibs. 

9"  13!  Ibs. 

Channels  of  weights  different  than  those  given  above  can  always  be  ob- 
tained at  the  mills  but  not  so  readily  as  those  given.  Channels  of  minimum 
section  can  always  be  obtained  more  readily  than  heavier  sections. 

Angles. — Angles  most  easily  obtained  from  the  mill. 

Even  legs.— 2^"  X  2^";  3"  X  3";  3%"  X3^";  4"  X  4";  6"  X  6". 

Uneven  legs.— 2^"  X  2" ;  3"X2H";  3V2"X3";  4"X3";  5"X3^"; 
6"  X  4". 

Angles  which  may  be  used  but  for  which  prompt  deliveries  cannot  be 
expected. 

Even  legs.— 2"  X  2";  2^4"  X  2^";  5"  X  5";  8"  X  8". 

Uneven  legs.— 3"  X  2";  3^"  X  2^";  4"  X  3^";  6"  X  3^". 

Angles  4"X3V2";  5"X4";  7"  X  3^"  and  8"  X  6"  are  very  difficult  to 
obtain. 

To  obtain  prompt  deliveries  as  few  sizes  and  shapes  as  practicable  should 
be  used  for  any  contract.  For  example  if  6"  X  4"  angles  are  used  6"  X  3^2" 
should  be  avoided,  and  vice  versa. 

Tees.— If  possible  the  use  of  Tees  should  be  confined  to  3"  X  3"  X  ft"  and 
2"  X  2"  X  5/16",  and  even  these  sizes  are  uncertain  of  delivery. 

Zees. — The  delivery  of  zees  is  uncertain  and  will  depend  upon  special 
rollings,  which  do  not  occur  frequently.  The  following  sizes  are  the  most  used, 
and  are  therefore  most  easily  obtained. 

Web.  Thickness. 

3"  i",  A"  and  i" 

4"  i",  A"  and  I" 

5"  A",  i"  and  ¥' 

6"  i",  i",  f",  I",  I"  and  i" 

Stock  Material. — The  Pennsylvania  Steel  Company  carries  the  following 
material  in  stock  in  30  ft.  lengths  for  use  in  its  structural  plant. 

Angles,  Even  Legs.  Angles,  Uneven  Legs. 

6"  X  6"  X  iV  and  i"  6"  X  4"  X  i",  &"  and  I" 

4"  X  4"  X  5"  and  TV'  5"  X  3*"  X  I",  TV  and  I" 

3*"  X  3*"  X  I"  and  iV  4"  X  3*"  X  A",  and  I" 

3"  X  3"  X  A",  f"  and  iV          3*"  X  3"  X  A"  and  f" 

3"  X  2*"  X  iV  and  f" 


STRUCTURAL   DRAWINGS,   ESTIMATES   AND   DESIGNS. 


Plates. 

X  i"  and  \" 
X  I"  and  \" 
and  \" 
and  \" 
and  i" 
and  \" 


20 
18" 

16"  X  f" 
15"  X  f" 
14"  X  i" 
13"  X  I" 
12"  X  f",  A"  and 
10"  X  i"  and  -fs" 
9"  X  i" 


Flats. 

7"  X  i" 

6"  X  t"  and  i" 
3i"  X  i",  4"  and  f  " 
3"  X  I"  and  &" 
2*"  X  i"  and  &" 
2i"  X  A"  and  f" 
2"  X  i"  and  &" 


CHAPTER   III. 
ESTIMATES  OF  STRUCTURAL  STEEL. 

GENERAL  INSTRUCTIONS.— When  an  estimate  of  the  structural  steel 
in  a  structure  is  to  be  made  the  man  in  charge  shall  immediately  examine  all 
of  the  data  furnished  to  see  that  he  has  sufficient  information  to  make  a  satis- 
factory estimate.  He  shall  fill  out  the  data  sheet  completely,  and  then  take  off 
the  quantities.  Use  only  the  standard  estimate  blanks  for  taking  off  material. 
The  author  has  found  the  estimate  blank  below  very  satisfactory. 


CROCKER  C&  KETCHUM 

Consulting  Engineers 


DENVER,  COLO. 


a  !60-Ft.5panHiqhwav Bridqe 
Logan  Irrigation  Co. 


Sheet  No 


Feb.t5.l9lg 


Ho. 

re.. 

DEICXIFTION 

LENOTH 

Wdfht 

Per  Ft. 

WEIOHT 

B*fd 

TOTAL 

WEIOHT 

IMiMMM 

D*U1U 

•&"££? 

4EMDP05T5 

L< 

y, 

each 

)  thus:- 

2 

6"C5@  II  VA* 

26 

i% 

11.25 

589 

1 

Cov.PI.  IZ^5/^ 

26 

5 

ins 

337 

2 

Bat.Pl.  ItxW 

1 

Op 

\m 

21 

4 

HinqePI.6?x^ 

0 

8 

5.33 

16 

4 

Pin  Pl.SxVa 

1 

3 

10.20 

51 

E 

Fill  PI.  6g'xf6 

0 

6 

1.38 

Z 

46 

Lac  Brs.  l^/fx'A." 

1 

1* 

1.49 

83 

5Z6 

Riv.  Hcl5.  For|'<j>  perlOO- 

85 

926 

258 

1184 

4 

4756 

Number  each  page  consecutively,  and  when  all  the  quantities  are  totaled 
prepare  a  summary  on  the  last  page.  Each  sheet  shall  have  the  sheet  number 
and  also  the  total  number  of  sheets  in  the  estimate,  for  example  9  of  20.  This 


ESTIMATES   OF    STRUCTURAL    STEEL.  33 

will  prevent  the  loss  of  a  page.  After  the  estimate  is  completely  taken  off 
another  man  shall  check  it.  When  checked  the  estimate  shall  be  extended  by 
the  checker,  each  sheet  being  immediately  totaled  up  as  extended.  The  exten- 
sions shall  then  be  checked  by  the  original  estimator,  who  also  prepares  a 
summary.  The  summary  is  then  checked  by  the  checker  and  the  estimate  is 
complete. 

The  estimate  should  be  practically  a  condensed  bill  of  material  of  the  work, 
and  should  be  so  clearly  made  that  a  reference  to  the  estimate  will  show  at  a 
glance  the  weight  of  all  the  principal  pieces.  Main  and  secondary  trusses,  main 
columns,  girders,  crane  girders,  etc.,  for  buildings,  and  trusses,  girders,  floor 
beams,  etc.,  for  bridges  should  be  taken  off  separately,  thus — I  truss,  6  required 
— and  shall  not  be  mixed  together  even  though  the  correct  weight  is  obtained. 
In  making  an  estimate  the  following  order  will  be  found  convenient. 

i.  MILL  BUILDINGS. — Trusses.— Top  chords,  lower  chords,  web  mem- 
bers, purlin  lugs,  gusset  plates,  connection  plates,  splice  plates,  eave  strut  con- 
nections, knee  braces  and  knee  brace  connections. 

Ventilator  Trusses. — Rafters,  posts,  web  members,  gusset  plates,  connec- 
tions to  trusses  and  purlin  lugs. 

Columns. — Column  angles,  web  plate,  base  plate  and  angles,  crane  seat  and 
cap.  Base  includes  anchor  bolts. 

Crane  Girders. — Flange  angles,  web  plate,  cover  plates,  end  stiffeners,  inter- 
mediate stiffeners,  fillers,  knee  braces  and  knee  brace  connections.  Rails,  splice 
bars,  clips  and  crane  stops. 

Miscellaneous. — Eave  struts,  lattice  girders,  purlins,  girts,  ridge  struts, 
lower  chord  struts,  column  struts,  rafter  bracing,  lower  chord  diagonals,  rein- 
forcing angles  for  purlins  used  as  rafter  struts,  and  sag  rods. 

Miscellaneous  Materials  Not  Structural  Steel. — Corrugated  steel  roofing 
and  siding,  louvres,  flashing  and  ridge  roll,  gutters,  conductors,  downspouts, 
ventilators,  stack  collars.  Windows,  doors,  skylights,  operating  device,  lumber, 
roofing,  brick  and  concrete. 

2.  OFFICE  BUILDINGS.— Floor  beams,  girders,  including  all  their  con- 
nections not  riveted  to  other  members.     Floors  should  be  estimated  separately 
using  a  multiplier  if  two  or  more  are  exactly  alike. 

Columns. — Columns  including  splices  and  connections  riveted  to  the 
columns.  If  columns  are  of  Bethlehem  "H"  sections,  it  should  be  so  noted  on 
the  estimate  summary.  Estimate  columns  in  tiers. 

Miscellaneous,  such  as  suspended  ceilings,  galleries,  penthouses,  lintels,  curb- 
angles,  canopies,  etc. 

3.  TRUSS  BRIDGES.— Truss  members  should  be  taken  off  separately  in 
order  that  the  estimate  will  show  at  a  glance  the  weight  of  any  main  member. 
Never  write  off  material  for  the  trusses  thus,  "  y2 — Truss — 4  Req'd." 

Stringers ;  floor  beams ;  portals ;  sway  trusses ;  upper  laterals ;  lower  laterals ; 
shoes,  masonry  plates,  anchor  bolts,  etc. 

A  convenient  order  can  easily  be  arranged  for  other  structures. 


34  STRUCTURAL   DRAWINGS,   ESTIMATES   AND   DESIGNS. 

INSTRUCTIONS  FOR  TAKING  OFF  MATERIAL.— Quantity  esti- 
mates shall  give  the  shipping  weights,  not  shipping  weights  plus  scrap.  Pin 
plates,  gusset  plates,  etc.,  shall  be  taken  off  as  equivalent  rectangular  plates. 
Large  irregular  plates  or  small  irregular  plates  which  occur  in  larger  numbers 
shall  have  the  exact  sizes  shown  in  the  estimate  and  should  have  their  weights 
accurately  calculated.  All  quantity  estimates  shall  be  made  out  with  black 
drawing  ink. 

The  following  colored  pencils  shall  be  used  in  estimating: 

Black. — In  taking  off  quantities,  all  check  marks  on  drawings  or  blue  prints 
shall  be  made  with  a  black  pencil. 

Red. — In  checking  "  quantities  taken  off "  all  check  marks  on  drawings, 
blue  prints  and  data  sheets  shall  be  made  with  a  red  pencil. 

Blue. — Blue  pencils  shall  be  used  for  checking  extensions,  also  for  making 
notes,  corrections,  alterations  or  additions  on  white  prints  or  tracings. 

Yellow. — All  alterations,  corrections  or  additions,  on  blue  prints  at  the  time 
of  estimating  shall  be  made  with  a  yellow  pencil. 

All  notes  on  blue  prints  or  drawings  in  regard  to  alterations,  corrections  or 
additions  shall  be  dated  and  signed  by  the  person  in  charge  of  the  estimate. 
In  general  all  work  shall  be  taken  off  in  feet  and  inches.  Lengths  of  bolts  shall 
be  given  in  feet  and  inches. 

CLASSIFICATION  OF  MATERIAL.— In  making  the  summary  steel 
and  iron  should  be  classified  as  follows: 

Bars,  including  plates  6"  wide  and  under,  rounds  up  to  3"  in  diameter  and 
squares  up  to  3"  on  a  side. 

Plates  (a)  Flats  over  6"  wide  up  to  and  including  100",  and   y^"  thick 

and  over. 
(&)  Flats  over  100"  wide  up  to  and  including  110". 

(c)  Flats  over  no"  wide  up  to  and  including  115". 

(d)  Flats  over  115"  wide  up  to  and  including  120". 

(e)  Flats  over  120". 
(/)  Plates  3/16"  thick. 
($r)   Plates  %"  thick. 
(h)  Plates  checkered. 
(*)  Plates  buckle. 

Angles  (a)  Having    both  legs  6"  wide  or  under. 

(t)  Having  either  leg  more  than  6"  in  width. 
(c)  Having  both  legs  less  than  3"  in  width. 
Channels  and  I-Beams 

(a)   Channels  and  beams  up  to  and  including  15"  in  depth, 
(fc)  Over  15"  in  depth. 

If   Bethlehem   sections   are  used   distinguish   between   "Bethlehem    Special 
I-Beams "  and  "  Girder  Beams,"  and  also  regarding  depths  as  above. 
Zees. 
Tees. 

Rails  (Separate  rails  under  50  Ibs.  per  yd.,  rails  over  100  Ibs.  per  yd.,  and 
girder  rails). 


ESTIMATES   OF   STRUCTURAL    STEEL.  35 

Rail  Splices. 

Iron  Castings. 

Steel  Castings. 

Nuts. 

devices  and  Turnbuckles. 

Pins,  rounds  from  3"  in  diameter  to  61/4"  in  diameter. 

Forgings,  rounds  over  6^4"  in  diameter. 

Bronze. 

Lead. 

Rivets  and  Bolts. 

Rivet  Heads. — Where  the  estimate  is  made  from  shop  drawings  the  actual 
number  of  rivet  heads  shall  be  determined.  The  weight  of  rivet  heads  in  per 
cent  of  the  total  weight  of  the  other  material  is  about  as  follows:  Purlins, 
girts  and  beams,  2  per  cent;  trusses  and  bracing,  4  per  cent;  plate  girders  and 
columns  of  4  angles  and  i  pi.,  5  per  cent ;  plate  girders  and  columns  with  cover 
plates,  6  per  cent;  box  girders  or  channel  columns  with  lacing,  7  per  cent; 
trough  floors,  8  to  10  per  cent. 

Bolts  are  usually  taken  off  in  the  estimate  when  they  occur,  and  entered  as 
rivets.  When  bolts  are  under  6"  in  length,  include  bolts  under  the  item  "  Bolts 
and  Rivets."  When  over  6"  in  length,  put  the  bolts  under  "  Bars." 

Miscellaneous  Materials. — Corrugated  Steel. — Always  give  the  number  of 
gage,  whether  painted  or  galvanized,  and  whether  iron  or  steel.  This  remark 
also  applies  to  louvres,  flashing,  ridge  roll,  gutters  and  conductors.  State 
whether  corrugated  steel  is  for  roofing  or  siding.  Roofing  shall  be  estimated  in 
squares  of  100  square  feet,  adding  three  feet  on  each  end  of  building  to  the 
distance  c.  to  c.  of  end  trusses  to  allow  for  cornice.  Allow  one  foot  overhang 
at  eaves.  Siding  shall  be  estimated  in  squares  of  100  square  feet,  adding  one 
foot  at  each  end  of  building  to  allow  for  corner  laps. 

Louvres  shall  be  estimated  in  square  feet  of  superficial  area,  stating  whether 
fixed  or  pivoted. 

Flashing  shall  be  estimated  in  lineal  feet  and  shall  be  taken  off  over  all 
windows  where  corrugated  sheeting  is  used  on  the  sides  of  building,  and  under 
all  louvres  and  windows  in  ventilators. 

Ridge  Roll  shall  be  estimated  in  lineal  feet,  adding  one  foot  to  the  distance 
center  to  center  of  end  trusses.  Ridge  roll  is  usually  taken  off  the  same  gage 
as  the  corrugated  steel  roofing. 

Gutters  and  conductors  shall  be  estimated  in  lineal  feet,  the  conductois 
usually  being  spaced  from  40  to  50  feet,  depending  upon  the  area  drained. 

Circular  ventilators  shall  be  estimated  by  number,  giving  diameter  and 
kind,  if  specified. 

Stack  collars  shall  be  estimated  by  number,  giving  diameter  of  stack. 

Windows  shall  be  estimated  in  square  feet  of  superficial  area,  taking  for  the 
width  the  distance  between  girts.  State  whether  windows  are  fixed,  sliding, 
pivoted,  counter-balanced  or  counter-weighted.  State  kind  and  thickness  of 
glass  and  give  list  of  hardware,  and  any  thing  else  of  a  special  nature. 

Doors  shall  be  estimated  in  square  feet;  state  whether  sliding,  lifting,  roll- 


36  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

ing  or  swinging.  Steel  doors  covered  with  corrugated  steel  shall  be  estimated 
by  including  the  steel  frame  under  steel  and  the  covering  with  corrugated  steel 
siding.  State  style  of  track,  hangers  and  latch. 

Skylights  shall  be  estimated  in  square  feet,  giving  kind  of  glass  and  frames. 

Operating  devices  for  pivoted  windows  or  louvres  shall  be  estimated  in 
lineal  feet. 

Lumber  shall  be  estimated  in  feet,  board  measure,  noting  kind.  Note  that 
lumber  under  i"  in  thickness  is  classified  as  i".  Above  i"  it  varies  by  l/^"  in 
thickness,  and  if  surfaced  will  be  %"  less  in  thickness,  i.  e.,  iW  sheathing  is 
actually  i>Ms"  thick,  but  shall  be  estimated  as  124".  Lumber  comes  in  lengths  of 
even  feet;  if  a  piece  io'-8"  or  n'-o"  is  required,  a  stick  i2'-o"  long  shall  be 
estimated.  In  using  lumber  there  is  usually  considerable  waste  depending  upon 
the  purpose  for  which  it  is  intended.  In  estimating  tongue  and  grooved  sheath- 
ing 10  to  20  per  cent  shall  be  added  for  tongues  and  grooves  and  from  5  to  10 
per  cent  for  waste,  depending  upon  the  width  of  boards  and  how  the  sheathing 
is  laid. 

Composition  roofing  or  slate  shall  be  estimated  in  squares  of  100  square 
feet,  allowing  the  proper  amount  for  overhang  at  eaves  and  gables  and  for 
flashing  up  under  a  ventilator  or  on  the  inside  of  a  parapet  wall. 

Tile  roofing  or  slate  shall  be  estimated  in  squares  of  100  square  feet,  adding 
5  per  cent  for  waste.  Include  in  an  estimate  for  tile  roof,  gutters,  coping, 
ridge  roll,  plates  over  ventilator  windows  and  plates  under  ventilator  windows, 
these  being  estimated  in  lineal  feet.  Flat  plates  for  the  ends  of  ventilators  shall 
be  estimated  in  square  feet. 

Brick  shall  be  estimated  by  number.  For  ordinary  brick  such  as  is  used  in 
mill  building  constructing  estimate  7  brick  per  square  foot  for  each  brick  in 
thickness  of  wall,  i.  e.,  a  9  in.  wall  is  two  bricks  thick  and  contains  14  brick  for 
each  square  foot  of  superficial  area. 

Always  note  whether  walls  are  pilastered  or  corbeled  and  estimate  the  addi- 
tional amount  of  brick  required.  If  walls  are  plain,  no  percentage  need  be  added 
for  waste,  but  if  openings  such  as  arched  windows  occur  add  from  5  to  10 
per  cent. 

Concrete  shall  be  estimated  in  cubic  yards.  Walls  or  ceiling  of  plaster  on 
expanded  metal  shall  be  estimated  in  squares  of  100  square  feet,  noting  thickness 
and  kind  of  reinforcement.  Reinforced  concrete  floors  shall  be  estimated  in 
square  feet  of  floor  area,  noting  thickness  and  kind  of  reinforcement.  Paving 
of  all  kinds  is  estimated  in  square  yards,  but  the  concrete  filling  under  the 
pavement  itself  is  estimated  in  cubic  yards.  Concrete  floor  on  cinder  filling  is 
usually  estimated  in  square  yards  specifying  its  proportions. 

CARD  OF  MILL  EXTRAS.— If  the  estimate  is  to  be  based  on  card 
rates  it  will  be  necessary  to  have  the  subdivisions  a,  b,  c,  d,  e,  f,  r,  etc.,  as 
follows : 

a  —  0.150.  per  Ib.  This  covers  plain  punching  one  size  of  hole  in  web  only. 
Plain  punching,  one  size  of  hole  in  one  or  both  flanges. 

b  =  0.250.  per  Ib.  This'  covers  plain  punching  one  size  of  hole  in  either 
web  and  one  flange  or  web  and  both  flanges.  (The  holes  in  the  web  and  flanges 
must  be  of  same  size.) 


ESTIMATES   OF   STRUCTURAL    STEEL.  37 

c^- 0.300.  per  Ib.  This  covers  punching  of  two  sizes  of  holes  in  web  only. 
Punching  of  two  sizes  of  holes  in  either  one  or  both  flanges.  One  size  of  hole 
in  one  flange  and  another  size  of  hole  in  the  other  flange. 

d  =  0.350.  per  Ib.  This  covers  coping,  ordinary  beveling,  riveting  or  bolting 
of  connection  angles  and  assembling  into  girders,  when  the  beams  forming  such 
girders  are  held  together  by  separators  only. 

e  =•  0.400.  per  Ib.  This  covers  punching  of  one  size  of  hole  in  the  web  and 
another  size  of  hole  in  the  flanges. 

f  =  0.150.  per  Ib.  This  covers  cutting  to  length  with  less  vibration  than 
±H  in. 

r  =  0.500.  per  Ib.  This  covers  beams  with  cover  plates,  shelf  angles,  and 
ordinary  riveted  beam  work.  If  this  work  consists  of  bending  or  any  unusual 
work,  the  beams  should  not  be  included  in  beam  classification. 

Fittings. — All  fittings,  whether  loose  or  attached,  such  as  angle  connections, 
bolts,  separators,  tie  rods,  etc.,  whenever  they  are  estimated  in  connection  with 
beams  or  channels,  to  be  charged  at  i.55c.  per  Ib.  over  and  above  the  base  price. 
The  extra  charge  for  painting  is  to  be  added  to  the  price  for  fittings  also.  The 
base  price  at  which  fittings  are  figured  is  not  the  base  price  of  the  beams  to 
which  they  are  attached  tut  is  in  all  cases  the  base  price  of  beams  15"  and  under. 

The  above  rates  will  not  include  painting,  or  oiling,  which  should  be  charged 
at  the  rate  of  o.ioc.  per  Ib.  for  one  coat,  over  and  above  the  base  price  plus  the 
extra  specified  above. 

For  plain  punched  beams  where  more  than  two  sizes  of  holes  are  used, 
o.i5c.  per  Ib.  should  be  added  for  each  additional  size  of  hole,  for  example, 
plain  punched  beams,  where  three  sizes  of  holes  occur  would  be  indicated  as ; 
c  -}-  o.i5c.,  four  sizes  of  holes;  e  +  o.3oc.  For  example:  a  beam  with  y%'  and 
24"  holes  in  the  flanges  and  $/%"  and  £4"  holes  in  the  web  should  be  included 
in  class  e. 

Cutting  to  length  can  be  combined  with  any  of  the  other  rates,  class  d  ex- 
cepted,  and  would  have  to  be  indicated;  for  example:  Plain  punching  one  size 
of  hole  in  either  web  and  one  flange,  or  web  and  both  flanges,  and  cutting  to 
length  would  be  marked  bf,  which  would  establish  a  total  charge  of  o.4oc.  per  Ib. 

Note  to  class  d. — No  extra  charge  can  be  added  to  this  class  for  punching 
various  sizes  of  holes,  or  cutting  to  exact  lengths;  in  other  words;  if  a  beam  is 
coped  or  has  connection  angles  riveted  or  bolted  to  it,  it  makes  no  difference 
how  many  sizes  of  holes  are  punched  in  this  beam,  the  extra  will  always  be  the 
same,  namely  0.35  c.  When  beams  have  angles  or  plates  riveted  to  them,  and 
same  are  not  half  length  of  the  beam,  figure  the  beams  as  class  d,  and  the 
plates  and  angles  as  beam  connections. 

Note  to  class  r. — This  rate  of  0.50  c.  per  Ib.  applies  to  all  the  material  making 
up  the  riveted  beam.  In  case  of  assembled  girders  in  which  one  of  the  beams 
should  be  classed  as  a  riveted  beam,  in  making  up  the  estimate,  figure  only  the 
beam  affected  as  included  in  class  "  r."  When  beams  have  angles  or  plates 
riveted  to  them  and  same  are  half  length  or  more  than  half  length  of  the  beam, 
figure  the  beams  as  class  "  r,"  including  the  plates  or  angles  and  rivets.  When 
18",  20",  or  24"  beams  are  in  "r"  class  keep  the  I's  separate  from  the  material 


38  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

(plates,  cast  iron,  separators,  angles  and  rivets)  which  should  go  under  heading, 
"  15"  I's  and  Under." 

Beams  should  be  divided  as  15"  I's  and  under,  and  18",  20"  and  24"  I's.  If 
there  are  only  one  or  two  sizes  of  beams  in  any  particular  class,  give  exact 
sizes,  instead  of  "  15"  I's  and  Under." 

In  estimating  channel  roof  purlins  classify  7"  channels  and  smaller  as  one 
punched;  8"  channels  and  larger  as  two  punched,  unless  they  are  shown  or 
noted  otherwise,  and  keep  separate  from  other  beams. 

No  extra  charge  can  be  added  to  curved  beams  for  riveting,  cutting  to 
length,  etc. 

Subdividing  work  into  a  large  number  of  classes  should  be  avoided;  it  is 
better  to  have  too  few  classes,  rather  than  too  many. 

The  only  subdivision  necessary  for  cast  iron  columns  are :  i"  and  over,  and 
under  i".  Columns  with  ornamental  work  cast  on  must  be  kept  separate. 

Round  and  Square  Bars. — In  estimating  round  and  square  bars  use  the 
standard  card  for  extras,  Table  I.  It  is  not  usual  to  enforce  more  than  one 
half  the  standard  card  extras  for  round  and  square  bars. 

Extras. — Shapes,  Plates  and  Bars: 
(Cutting  to  length) 

Under  3  ft.  to  2  ft.,  inclusive  0.25  cts.  per  Ib. 

Under  2  ft.  to  i  ft.,  inclusive 0.50  cts.  per  Ib. 

Under   i    ft 1.55  cts.  per  Ib. 

Extras — Plates  (Card  of  January  7,  1902) : 

Base  \  in.  thick,  100  in.  wide  and  under,  rectangular  (see  sketches). 

Weights — see  Manufacturer's  Standard  Specifications,  Carnegie  or  Cambria 
Hand-books. 

Per  ioo  Lbs. 

Widths — ioo  in.  to  no  in $  .05 

no  in.  to  115  in 10 

115  in.  to  120  in 15 

120  in.  to  125  in 25 

125  in.  to  130  in 50 

Over  130  in i.oo 

Gages  under  -k  in.  to  and  including  i3s  in 10 

Gages  under  i3g  in.  to  and  including  No.  8 15 

Gages  under  No.  8  to  and  including  No.  9 25 

Gages  under  No.  9  to  and  including  No.  10 30 

Gages  under  No.  10  to  and  including  No.  12 40 

Complete  circles 20 

Boiler  and  flange  steel 10 

Marine  and  fire  box 20 

Ordinary  sketches   10 

(Except  straight  taper  plates,  varying  not  more  than  4  in.  in  width  at  ends, 
narrowest  end  not  less  than  30  in.,  which  can  be  supplied  at  base  prices.) 


STRUCTURAL   ESTIMATES. 


TABLE   L. 


39 


STANDARD  CLASSIFICATION  OF  EXTRAS  ON  IRON  AND  STEEL  BARS.* 

Rounds  and  Squares. 
Squares  up  to  d$  inches  only.    Intermediate  sizes  take  the  next  higher  extra. 

Per  ioo  Lbs. 

f   to  3      in  .....................................................  Rates 

i   to     ii  "     ...............................................  .....  $0.10  extra. 

I     tO      ft    "      .....................................................  20  " 

&  "    .....................................................  40  " 

i  "  .....................................................  50  " 

ft  "     .................................  ....................  60  " 

i  and  392  "  .....................................................  70  " 

3?2  "        ....................................................        I.OO  " 

ft  "      ....................................................      2.00  " 

3ft  to  3*     "     .........................  ............................  15  " 

3ft  to  4      "     .....................................................  25  " 

4ft  to  4*     "     .....................................................  30  " 

4ft  to  5      "     .....................................................  40  " 

5*    to  5?     "     .....................................................  50  " 

5i    to  6      "     .....................................................  75  " 

6£    to  6*    "     ....................................................     i.oo  " 

61    to  7i    "     ....................................................     1.25  " 

Flat  Bars  and  Heavy  Bands. 

Per  ioo  Lbs. 

i      to    6     in.  x  I  to      I      in  .....................................  Rates. 

i      to    6      "  x  i  and     ft  "      ...................................  $0.20  extra. 

H  to      if  "  x  §  to        I   "      .....................................  40  " 

ii  to      il  "  x  i  and     ft  "      .....................................  50  " 

i9s  and     f    "  x  i  to        \    "      .....................................  50  " 

T9s  and     f    "  x  i  and     ft  "      ............  ..  ........................  70  " 

\  "  x  §  and     T^  "      .....................................  oo  " 

*  "x^and     ft"      ....................................     1.  10  " 

ft  "  xf  "      ....................................     i.oo  " 

ft  "xiand     ft"      ....................................     1.20  " 

I  "  x  i  and     ft  "      ..........................  .  .........     1.50  " 

ij     to    6    in.  xi^toiftin  ......................................  10  " 

IF     to     6     "  x  ii     to  i*     "        ...............  ......................  20  " 

if    to    6    "xil    to  2!     "       .....................................  30  " 

3^    to    6    "  x  3      to  4      "       .....................................  40  " 

*  Adopted  August,  1902. 


4O  STRUCTURAL   DRAWINGS,   ESTIMATES   AND   DESIGNS. 

Light  Bars  and  Bands. 

Per  100  Lbs. 

ii    to     6      in.  x  Nos.  7, 8, 9  and  &  in $0.40  extra. 

li     to     6      in.  x  Nos.  10,  n,  12  and  i  in 60 

i      to      iik  in.  x  Nos.  7, 8, 9  and  iV  in 50  ' 

i      to      iik  in.  x  Nos.  10,  n,  12  and  i  in 70 

II  to       it  in.  x  Nos.  7, 8, 9  and  A  in 70  ' 

II  and     i!  in.  x  Nos.  10,  1 1,  12  and  %  in 80 

iJ  and    f    in.  x  Nos.  7, 8,  9  and  ^  in i.oo  ' 

ii  and    f    in.  x  Nos.  10,  n,  12  and  i  in 1.20  ' 

i9g  and    f    in.  x  Nos.  7, 8,  9  and  &  in 1.20 

T95  and    f    in.  x  Nos.  10,  n,  12  and  I  in 1.30  ' 

\  x  Nos.  7, 8,  9  and  &  in 1.30  _" 

i  x  Nos.  10, 1 1, 12  and  £  in i  .50  ' 

&  x  Nos.  7, 8, 9  and  i^  in 1.80  " 

Je  x  Nos.  10,  n,  12  and  i  in 2.10  " 

§  x  Nos.  7, 8,  9  and  &  in i.oo  " 

I  x  Nos.  10,  n,  12  and  i  in 2.40  " 

CORRUGATED  STEEL.— Corrugated  steel  is  rolled  to  U.  S.  standard 
gage.     The  weights  of  flat  steel  and  corrugated  steel  for  different  gages  and 

Corrugated  Roof  Steel 
Side  Lap  2  Corrugations 

-*t*  -  Covers £/i" 


i      2d  w/'tfe  before  CGrrug&f/ 


\z& 

(a) 

Special  Cor-  Roof  Steel 
Side  Lap  \k  Corrugations 
—  Covers  24"-  >h  -  Covers  24' 


•*  £^  "-1         h  -30  "w/tfe  before  corrug&f/ng 

r-/7//(<  ••    afrer 
£nc/Lap  for  Roof  6" 
(b) 

Corrugated  Siding  Steel 
Side  Lap  I  Corrugation 
—  Covers  24"-^-  Covers  14  "  -~- 


\*  Zd'w/tfe  before  ccrrugaf  ing 
^26"  »   after 
End  Lap  for5/tfes  4  " 

(CJ 
FIG.  21.    DETAILS  OF  CORRUGATED  STEEL. 


STRUCTURAL    ESTIMATES. 


thickness  are  given  in  Table  II.    This  cable  is  for  flat  sheets  and  for  corrugated 
steel  with  corrugations  approximately  2^  in.  wide  and  ^  in.  deep. 

TABLE   II. 
WEIGHT  OF  FLAT  AXD  CORRUGATED  STEEL  SHEETS  WITH  2^-iNCH  CORRUGATIONS. 


Gage  No. 

Thickness  in 
Inches. 

Weight  per  Square  (100  Sq.  Ft.). 

Flat  Sheets. 

Corrugated  Sheets. 

Black. 

Galvanized. 

Black  Painted. 

Galvanized. 

16 
18 

20 

rf 

26 

28 

.0625 
0500 
•OJ75 
.0313 
.0250 
.0188 
.0156 

250 
200 
ISO 
125 
100 

75 
63 

266 
216 
166 
141 
'116 
91 
79 

275 
220 

165 

138 

III 

84 
69 

291 
236 

182 

99 
86 

Corrugated  siding  and  roofing  is  rolled  as  shown  in  Fig.  21.  The  special 
corrugated  steel  in  (b)  Fig.  21  is  commonly  used  for  roofing,  and  the  corrugated 
steel  in  (c)  is  used  for  siding. 


* 


f 

-V\ 


If  side  laps  ofroof/ngr  dre  to  be 
riveted,  use  closing-  rivets  spaced 
not  more  than  /v  c.  to  c. 
&£„ 

Straps  every  4-0"^ 

Bottom 


Box  Cornice  Gutter 

and 
Truss  ffnchor 


r^r^j^j-^r^ 


•  Laps  for  fob.  £orr.5tee/5iding  \ 

\— Closing-Rivet    ^^w^end/ap '/£/ 'siding     £ 


Roof  sheet  turned  c/p 

/-Ovt/ooter      ^  **£*** 
rmtsh  of  vent.  End 


flashing?  turned  in  to 
.' joints  of  brick  and  stepped 
\al 


Purlin- 
Clinch  Rivet' 


6ab/eF;'nish  -  .  6abfe  finish  with  Parapet  Waff 

Gab/eF/nish  with  drick  l*va// 

FIG.  22.     STANDARD  DETAILS  FOR  CORRUGATED  STEEL. 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


The  standard  stock  lengths  vary  by  single  feet  from  4  ft.  to  10  ft.  Sheets 
can  be  obtained  as  long  as  12  ft,  but  are  special  and  cost  5  per  cent  extra  and 
will  delay  the  order. 

The  purlins  should  be  spaced  for  corrugated  steel  without  sheathing  for  a 
load  of  30  Ibs.  per  sq.  ft.  on  the  roof,  and  25  Ibs.  per  sq.  ft.  on  the  sides,  as 
given  in  Fig.  23. 

120 


« 


$r 


W=  Total  safe  load. 

Working  stress  - 12000  tb£» 
h* Depth  ofcorrugation%l 
t>  *  Width  of  sheet*  ins. 
t -Thickness  of 'sheet ,  ins. . 
1  • 'Clear  spon%  ins- 


4  5 

>,Z.,/>7/fc 

FIG.  23.    SAFE  LOADS  FOR  CORRUGATED  STEEL. 

Fastenings  for  Corrugated  Sheeting. — Corrugated  steel  is  fastened  to 
purlins  and  girts  usually  by  the  following  fasteners. 

Straps. — These  are  made  of  No.  18  U.  S.  gage  steel,  ^  of  an  in.  wide. 
These  straps  pass  around  the  purlins  and  are  riveted  to  the  sheets  at  both  ends 
by  3/16"  diameter  rivets,  Y%  in.  long ;  or,  they  may  be  fastened  by  bolts.  Order 
one  strap  and  two  rivets,  or  bolts,  for  each  lineal  foot  of  girt  or  purlin,  to 
which  the  corrugated  steel  is  to  be  fastened,  and  add  20  per  cent  to  the  number 
of  rivets  for  waste,  and  10  per  cent  to  the  straps  or  the  bolts.  One  thousand 
rivets  will  weigh  6  Ibs.;  one  bundle  of  hoop  steel  will  weigh  50  Ibs.  and  con- 
tains 400  lineal  feet. 

Clinch  Rivets  or  Nails. — These  are  special  rivets  or  nails  made  of  No.  9 
Birmingham  gage  wire,  which  clinch  around  the  edge  of  the  angle  iron  or 
channel  and  are  used  for  fastening  the  steel  sheathing  to  steel  purlins  or  girts. 
They  are  of  the  following  lengths  and  widths. 

TABLE  OF  CLINCH  NAILS. 


L  Purlin  leg 
Length 
No.  per  Ib. 

5" 
32 

4" 
6" 
29 

5" 
7" 
23 

6" 
8" 

21 

7" 
9" 
18 

C  Purlin  leg 
Length 
No.  per  Ib. 

3" 
6" 
29 

4" 
7"  or  8" 

21 

f 

18 

6" 

10" 

16 

7" 
n" 

H 

STRUCTURAL   ESTIMATES. 


43 


Order  two  rivets  to  each  lineal  foot  of  purlin  or  girt  to  which  the  corru- 
gated steel  is  to  be  fastened  and  add  10  per  cent  for  waste. 

Clips  and  Bolts. — These  are  used  for  fastening  corrugated  steel  to  steel 
purlins  or  girts.  Clips  are  made  of  No.  16,  i*/2  in.  steel,  about  2l/2  in.  long,  and 
are  slightly  crimped  at  one  end,  to  go  over  the  flange  of  the  purlin.  The  bolts 
are  of  the  same  diameter,  and  have  the  same  head  as  the  clinch  rivets,  except 
that  they  are  supplied  with  threads  and  nut,  and  are  about  I  in.  long.  These 
clips  and  bolts  should  not  be  used  excepting  in  special  cases,  where  the  regular 
fastenings  cannot  be  easily  applied. 

In  cases  where  flashing,  cornice  work,  and  several  thicknesses  of  metal  are 
to  be  fastened  at  one  point,  rivets  or  bolts,  other  than  standard  lengths  given 
will  be  needed.  Closing  rivets  */2  in.  long  and  bolts  il/2  in.  long  will  usually 
answer  these  cases. 

If  side  laps  of  corrugated  steel  are  to  be  riveted,  rivets  should  be  ordered, 
one  for  each  lineal  foot  of  side  lap,  plus  20  per  cent  for  waste. 

If  corrugated  steel  is  to  be  fastened  to  wooden  purlins  or  timber  sheathing, 
order  8d  barbed  nails  for  roofing  and  for  siding.  These  nails  should  be  spaced 
one  foot  apart,  for  both  end  and  side  laps;  add  20  per  cent  for  waste.  96  8d 
barbed  nails  weigh  I  Ib. 

Corrugated  steel  for  roofing  should  be  laid  with  two  corrugations  side  lap 
if  standard  or  i^  corrugations  side  lap  if  special,  and  6  in.  end  lap.  Corru- 
gated steel  for  siding  should  have  one  corrugation  side  lap  and  4  in.  end  lap. 

Louvres. — Weights  of  Shiffkr  louvres  of  black  iron  or  steel  are  as  follows : 


Gage  No. 
20 
22 


Weight  per  Square  Foot. 

2.7  Ibs. 
2.0  Ibs. 


The  weight  is  obtained  from  Fig.  24,  as  follows : 


FIG.  24.    LOUVRES. 


Louvres  are  estimated  in  square  feet  =  2h  X  length. 

To  get  weight  multiply  area  by  (1.7  X  weight  per  sq.  ft.  of  flat  of  material 
used). 

Ridge  Roll. — Ridge  roll  is  ordinarily  of  same  gage  as  roofing  and  black  or 


44  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


galvanized  to  correspond  with  same.    Ridge  roll  is  usually  made  from  an  18  in. 
flat  sheet. 

Gage  No.  Wt.  per  lin.  ft. 

2O 

22  2.0  Ibs.  ^  Black  Iron  or  Steel. 

24 


2.4  Ibs.  \ 
2.0  Ibs.  > 
1.6  Ibs.  3 


Gutters. — Eave  or  valley  gutters  should  always  be  galvanized.     Valley  gut- 
ters should  be  No.  20  gage.    Eave  gutters  and  conductors  No.  22  gage.    Gutters 

should  be  sloped  not  less  than  I  in.  in  15  feet. 

• 

WEIGHTS  OF  EAVE  GUTTERS  AND  CONDUCTORS  OF  GALV.  IRON  OR  STEEL. 


Span  of  Roof. 

Size  of  Gutter. 

Wt.  per  ft. 

Size  and  Spacing 
of  Conductor. 

Wt.  per  lin. 

ft.  No.  22. 

up  to    50' 
50  to    70' 
70  to  100' 

6",  No.  22 
7",  No.  22 
8",  No.  22 

1.8  Ibs. 
1.9  Ibs. 
2.1  Ibs. 

4  in.  every  40'  o" 
5  in.  every  40'  o" 
5  in.  every  40'  o" 

1.5  Ibs. 
2.1  Ibs. 
2.3  Ibs. 

CHAPTER   IV. 
DESIGN  OF  STEEL  STRUCTURES. 

Drawings. — Designs  shall  be  made  on  standard  sized  sheets.  A  scale  of 
^  in.  to  i  ft.  shall  be  a  minimum,  a  larger  scale  being  used  if  practicable.  Give 
such  distances  on  both  plan  and  cross-section  that  the  dimensions  of  either  can 
be  understood  without  reference  to  the  other. 

DESIGNS   OF  MILL   BUILDINGS. 

Loads. — All  roof  loads,  snow  loads,  wind  loads,  floor  loads,  wheel  loads  and 
spacing  for  cranes,  and  in  case  of  bins,  the  weight  per  cubic  foot  and  the  angle 
of  repose  of  the  material  shall  appear  on  the  design  drawings. 

Diagrams. — Draw  as  many  sections  as  are  necessary  to  show  all  transverse 
bents  and  trusses,  a  plan  of  lower  chord  bracing,  and  views  to  indicate  framing 
and  side  views  when  necessary  to  give  location  of  doors  and  windows.  When  a 
sectional  view  is  shown,  always  mark  the  location  of  the  sections  on  the  plan. 
When  two  buildings  frame  into  each  other  the  design  should  always  indicate 
the  framing  for  the  connections,  drawing  additional  sections  if  required. 

Stresses. — The  stresses  in  all  members  of  transverse  bents,  trusses  and 
latticed  and  plate  girders,  and  the  loads  on  all  main  building  columns  shall  be 
given  on  the  design  drawings.  Give  maximum  bending  moment  and  maximum 
shear  in  all  crane  girders,  plate  girders,  and  floor  girders  and  columns. 
Maximum  shear  and  bending  moment  shall  be  given  for  all  stringers  or  I-Beams 
used  as  floor  or  crane  girders. 


DESIGNS   OF   STEEL   STRUCTURES.  45 

Notes. — Material  (whether  O.  H.  (open  hearth)  or  Bessemer,  soft,  medium 
or  structural  steel);  specifications  (name  and  date;  size  of  rivets  and  holes, 
reamed  or  punched  full  size). 

Angle  Members. — In  all  cases  where  two  unequal  legged  angles  are  used 
as  main  members,  show  the  direction  in  which  the  outstanding  legs  are  turned 
by  giving  the  dimension  of  the  leg  appearing  in  elevation,  or  by  exaggerating 
the  longer  leg. 

Sections. — Give  sections  of  all  members  used  in  the  structure.  Whenever 
two  or  more  columns  or  other  members  in  different  locations  have  the  same 
section,  either  note  it,  or  mark  the  section  on  each  one.  For  a  column  of  special 
.make-up  show  a  cross  section. 

Dimensions. — The  following  dimensions  should  be  given:  (i)  Height  of 
lower  chord  of  trusses  from  floor  level;  (2)  elevation  of  top  of  crane  rail  with 
clearance;  (3)  distance  c.  to  c.  of  crane  rail  with  clearance;  (4)  distance 
b.  to  b.  of  angles  of  all  main  columns;  (5)  pitch  of  trusses  or  height  of  same 
at  heel  and  slope  of  upper  chord;  (6)  width  and  height  of  ventilator;  (7) 
length  of  bays;  (8)  distance  c.  to  c.  of  building  columns;  (9)  location  and  size 
of  stacks;  (10)  location  and  size  of  openings  and  circular"  ventilators ;  (n) 
thickness  of  all  walls,  and  relation  to  center  line  of  columns. 

Windows. — Give  size  and  number  of  lights  and  height  of  windows.  Show 
location  of  all  windows.  State  whether  pivoted,  sliding,  counter-balanced  or 
fixed,  and  whether  continuous.  State  kind  of  glass. 

Doors. — Give  dimensions  (width  by  height)  and  state  whether  wood  or 
steel,  swinging,  lifting,  rolling  or  sliding.  State  style  of  track,  hangers  and  latch. 

Louvres. — Note  depth  on  design,  and  whether  wood  or  metal,  fixed  or 
pivoted.  If  metal  give  gage  and  kind  of  same. 

Corrugated  Steel. — Give  gage  and  kind  of  all  corrugated  sheeting,  painted 
or  galvanized;  method  of  fastening,  lining,  etc. 

Gutters  and  Conductors. — Show  gutters,  conductors  and  downspouts  where 
necessary  and  give  size  and  kind  and  thickness  of  metal,  methods  of  fasten- 
ing, etc. 

Circular  Ventilators. — Show  location  on  design  and  note  size  and  kind. 

Roofing. — Give  kind  of  roofing  material,  and  thickness  of  sheathing  when 
used. 

Notes. — Note  on  design  the  section  of:  (a)  Purlins  and  form  where 
trussed;  (b)  girts;  (c)  sag  rods;  (d)  lateral  bracing;  (e)  end  columns;  (f) 
window  posts;  (g)  door  posts. 

Connections.— In  making  a  design  be  sure  that  all  clearances  and  connec- 
tions with  adjoining  structures  are  properly  provided  for  and  that  all  dimensions 
necessary  for  detailing  of  same  are  given  on  the  design. 

35 


46  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

DESIGNS  OF  PLATE  GIRDER  BRIDGES. 

Loads.— Give  assumed  dead,  live  and  wind  loads,  and  show  diagram  of 
wheel  loads. 

Diagram  and  Views. — Show  an  elevation  of  girder  with  stiffeners,  a  plan 
with  lateral  bracing,  and  a  half  end  view  and  a  half  intermediate  section. 

Stresses. — Give  maximum  bending  moments  and  maximum  shears,  maxi- 
mum stresses,  required  and  actual  net  area  of  flanges,  noting  number  of  rivets 
deducted,  and  required  net  and  actual  gross  areas  of  webs. 

Dimensions. — The  following  dimensions  should  appear  on  all  plate  girder 
designs.  Distance  b.  to  b.  of  end  angles,  or  distance  out  to  out  of  girders, 
c.  to  c.  of  bearings,  back  wall  to  back  wall,  or  c.  to  c.  of  piers,  b.  to  b.  of  flange 
angles,  spacing  of  girders  and  track  stringers,  base  of  rail  to  masonry,  end  of 
steel  to  face  of  back  wall,  angle  of  skew  if  any,  and  grade  of  base  of  rail. 

For  girder  bridges  on  curves  give  the  curvature  and  super-elevation  of 
outer  rail  and  distance  from  top  of  masonry  to  base  of  low  rail.  Give  elevation 
of  grade  and  of  masonry  on  a  vertical  line  through  center  of  end  bearing. 

Rivet  Spacing. — Note  on  the  elevation  of  girders  the  spacing  of  rivets  con- 
necting flange  angles  to  web,  changing  spacing  at  stiffener  points.  Give  number 
of  rivets  in  single  shear  for  end  connections  of  all  laterals  and  cross  frames. 

Shoes  and  Pedestals. — Give  maximum  reaction,  required  and  actual  area 
of  masonry  plate,  with  allowable  pressure  on  masonry.  Note  size  of  bed  plate, 
and  show  in  position  with  location  of  holes  for  anchor  bolts.  Note  size  and 
number  of  rollers  for  expansion  pedestal,  and  also  whether  pedestal  is  built, 
cast  iron  or  steel. 

Expansion  Points. — Mark  fixed  and  expansion  po:nts  and  show  whether 
pedestals  or  bearing  plates  are  to  be  used. 

Stiffeners. — Show  end  and  intermediate  stiffeners  on  elevation  of  girder, 
giving  sections  and  stating  whether  fillers  are  used,  or  stiffeners  crimped. 

Super-elevation. — If  the  bridge  be  on  a  curve,  show  how  the  super-eleva- 
tion of  the  outer  rail  is  to  be  cared  for,  whether  by  tapering  ties,  or  changing 
height  of  pedestal  or  masonry  plate. 

Track. — Show  track  in  place,  noting  such  information  as  size  and  notching 
of  ties  and  guard  timbers  and  manner  of  connecting  timber  deck  to  the  girder. 
For  through  girder  always  show  clearance  diagram  with  dimensions. 

Notes. —  (a)  Material  (whether  O.  H.  (open  hearth)  or  Bessemer,  soft, 
medium  or  structural  steel)  ;  (b)  specifications  (name  and  date)  ;  (c)  size  of 
rivets  and  holes,  reamed  or  punched  full  size. 

DESIGNS  OF  TRUSS  BRIDGES. 

Loads. — Always  give  the  following  assumed  loads  on  the  stress  sheets. 

Dead  Loads. —  (a)  Weight  of  track  in  Ibs.  per  lin.  ft.  of  track;  (b)  weight 
of  trusses  and  bracing  per  lin.  ft.  of  bridge;  (c)  weight  of  stringer  and  stringer 
bracing  per  lin.  ft.  of  bridge;  (d)  weight  of  floor  beams  per  lin.  ft.  of  bridge. 


DESIGNS   OF   STEEL   STRUCTURES.  47 

Live  Load. —  (Diagram  of  wheel  loads.) 

Wind  Load. 

Diagrams. — In  general,  the  design  shall  show  an  elevation  of  the  truss, 
plan  of  top  lateral  bracing,  plan  of  bottom  lateral  bracing  and  stringer  bracing, 
half  end  view  showing  portal,  half  intermediate  view,  or  as  many  intermediate 
views  as  are  necessary  to  show  intermediate  sway  frames.  The  end  view  shall 
show  track  in  place  with  information  similar  to  that  for  plate  girders.  The 
design  of  a  pin  connected  bridge  shall  show  the  sizes  of  pins  and  the  arrange- 
ment of  the  members  at  all  panel  points. 

Stresses. — Give  the  stresses  in  all  members  of  trusses  as  follows:  D.  L. 
(Dead  Load) ;  L.  L.  (Live  Load)  ;  I.  (Impact)  ;  C.  (Curvature)  ;  W.  (Wind 
Stresses).  Also  total  stresses. 

Always  use  the  minus  sign  for  tensile  stress  and  the  plus  sign  for  com- 
pressive  stress.  Compute  and  give  traction  stresses  for  viaduct  towers. 

For  stringers  and  floor  beams  give  the  bending  moment  and  shear  and 
stresses  in  the  same  manner  as  for  plate  girders. 

General  Dimensions. — The  most  important  dimensions  are,  number  of 
panels  and  length,  depth  of  truss  at  every  panel  point  if  upper  chord  is  curved, 
distance  c.  to  c.  of  trusses,  distance  base  of  rail  to  masonry,  distance  center  of 
end  pin  to  masonry,  distance  c.  to  c.  of  end  pins  and  face  to  face  of  masonry, 
or  c.  to  c.  of  piers.  If  the  bridge  be  on  a  curve,  give  the  degree  and  show 
direction  of  curvature,  the  distance  of  base  of  low  rail  to  masonry,  and  the 
super-elevation  of  outer  rail.  Note  that  greater  clearances  are  required  on 
curves.  Show  the  clearance  line  and  line  of  base  of  rail  in  the  elevation  of  truss. 

Compression  Members. — Give  the  actual  unit  stress,  the  allowable  unit 
stress,  radius  of  gyration,  moment  of  inertia,  actual  and  required  area,  eccen- 
tricity and  cross-section. 

Tension  Members. — Give  allowable  and  actual  stresses,  the  required  and 
actual  net  area.  For  built  sections  give  number  of  holes  deducted  for  rivets 
in  obtaining  net  area,  and  radius  of  gyration. 

Sections. — Give  section  of  every  member  and  thickness  of  all  gusset  plates. 
Always  give  size  of  lacing  bars,  and  state  whether  single  or  double  lacing  is 
required. 

Built  Sections. — On  all  built  sections  give  depth  of  section,  and  in  using 
plate  and  angle  sections,  make  the  web  y2"  less  in  width  than  the  depth  of 
section. 

Angles  with  Unequal  Legs.— In  any  member  composed  of  one  or  more 
angles  with  unequal  legs,  show  clearly  the  direction  in  which  the  long  or  short 
leg  is  turned. 

Rivets. — Note  the  number  of  rivets  to  be  used  for  end  connections  of  all 
members,  and  give  the  number  of  rivets  in  single  shear  required  at  end  con- 
nection of  track  stringers. 

Shoes  or  Pedestals. — Give  maximum  reaction,  required  and  actual  area  of 
masonry  plate,  with  allowable  pressure  on  masonry.  Note  size  of  bed  plate, 


48  STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 

and  show  in  position  with  location  of  holes  for  anchor  bolts.  Note  size  and 
number  of  rollers  for  expansion  pedestal,  and  also  whether  pedestal  is  built, 
cast  iron  or  steel. 

Camber. — The  amount  of  camber  should  be  shown  on  the  design. 

Notes. — Same  as  for  Plate  Girders. 


CHAPTER   V. 

TABLES  AND  STRUCTURAL  STANDARDS. 
CONTENTS. 

Table   I.  Standards  for  Lacing  Bars. 

Table   2.  Standards  for  Rivets  and  Riveting. 

Table   3.  Standards  for  Riveting. 

Table  4.  Standards  for  Riveting. 

Table   5.  Standard  Rivet  Spacing  for  Caulking. 

Table  6.  Purlin  Details. 

Table   7.  Carnegie  I-Beams. 

Table   8.  Carnegie  I-Beams. 

Table   9.  Carnegie  Channels. 

Table  10.  Carnegie  Z-Bars. 

Table  n.  Weights  of  Angles. 

Table  12.  Areas  of  Angles. 

Table  13.  Upsets  for  Round  and  Square  Bars. 

Table  14.  Clevises. 

Table  15.  Sleeve  Nuts  and  Turnbuckles. 

Table  16.  Loop  Bars. 

Table  17.  Eye-Bars. 

Table  18.  Bridge  Pins  with  Lomas  Nuts. 

Table  19.  Standard  Cotter  Pins. 

Table  20.  Standard  Cast  O.  G.  Washers. 

Table  21.  Allowable  Bending  Moment  in  Pins. 

Table  22.  Shearing  and  Bearing  Value  of  Rivets. 

Table  23.  Areas  to  be  Deducted  from  Plates. 

Table  24.  Buckle  Plates. 

Table  25.  Typical  Hand  Cranes. 

Table  26.  Typical  Electric  Cranes. 

Table  27.  Table  for  Rivet  Spacing. 

Table  28.  Table  for  Rivet  Spacing. 

Table  29.  Anchor  and  Tie  Rods. 

Table  30.  Channel  Columns. 


STRUCTURAL    TABLES   AND   STANDARDS. 


49 


TABLE   i. 
STANDARDS  FOR  LACING  BARS. 


MAXIMUM  DISTANCE  c    IN  FEET  AND  INCHES 

FOR  GIVEN  THICKNESS    t    OF  LACE  BAR 


THICKNESS 
OF  BAR 

SINGLE 

LACING 

DOUBLE 

LACING 

THICKNESS 
OF  BAR 

t 

1             C' 

0 

t           C 

t 

INCHES 

t^So 

*—&> 

t~7S 

INCHES 

% 

2-   1 

2-7* 

3-   It 

3-101 

% 

%« 

1  -10J 

2-4 

2-  9| 

3-  6* 

%6 

^ 

1-  8 

2-1 

2-  6 

3-  li 

% 

7/i« 

1-  5i 

l-9i 

2-   2* 

2-  8! 

%« 

% 

1-  3 

1-61. 

l-10i 

2-  4 

% 

%« 

1-  01 

1-  6! 

1-ltt 

*He 

H 

0-10 

1-Oi 

1-   3 

1-  61 

% 

rivet 


rivet 


*  rivet 


rivet 


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fy**>4 
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r.J£.| 

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-{r!-For$"rivete 

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L                            6                         W 

{•"  '  

1                                 1 

1 

o)'  (o                 o 

)(o             °)i 

DISTANCE 

/N  INCHES    TO 

BE  ADDED    TO 

LENGTH   c 

FOR  FINISHED  LENGTH    ft 


FOR  ORDERED  LENGTH 


'WIDTH 

OF  BAR 

INCHES 

%'/ 

DIAMETER  OF  RIVET 

DIAMETER  OF  RIVET 
%//                 %/x               %"               76y/ 

W/DTH 
OF  S<4/? 

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31 

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3 

2% 

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it 

2! 

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5O 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE  2. 

STANDARDS  FOR  RIVETS  AND  RIVETING. 


6A6ES 

/n  inches 


u? 


/fox 


Let 


±__^j          NJ 

PROPORTIONS  Of 
in  inches 


Diameter 

of 
5hank 


full  head 


Diameter  Height 


Gounfersunk 


Diameter  Depth 


When  &"L  exceeds  3  " 


' 


SSL 

64 


/6 


17 


5L 
64 


M/WMVM 
RIVfT 5PAC/N6 


Size  off? wet  Min.  Didana 


inches 


inches 


II 

76 


32 


MIN/MUM  5TA66ER 


1 


RIVET5 


'1 


'nchesForffih 


b 
/r?  inches 


n/ 
1  n 


'nches  For j$  Rivet  For/ft/ef 


b 
In  inches 


15 
16 


' 


MINI  nun 
BUTTON5ET5 


Forffbets  less  than^ 

" 


' 


// 


//I 


15 
76 


R/VET5  IN  Cft/MPED  /? 


wchoretLsJvfneYerJenthanl 


'i 


STRUCTURAL   TABLES    AJSTD   STANDARDS. 


TABLE   3. 
STANDARDS  FOR  RIVETING. 


DISTANCE  $TO$OF 


VALUES  OFXF02  VAPY/N6  VPLUES  OF  fl  ffND  B. 


VALUti 
OFB 


/ 


VALUES  OFfi 


/I 


2k 


2 


4 


ti 


2k 


2 


o 
r/ 


4 


44 


2 


2 


2% 


2k 


44 


4 


/I 


4 


44 


4 


4 


2% 


2% 


2% 


4 


4 


## 


4 


4.4 


NOTE '--Valuer  be/ow  or  to  the  right  of  upper  zigzag  line  are  large  enough  For\ 
*         *    * - '•  »   *      "      "  second     ' 
>t         „.,,*»       *      "lower       ' 


nun 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE  4. 

STANDARDS  FOR  RIVETING. 


-o- 
-fr 


inches 


A 


/I 


/I 


bin  inch  es 


r/v. 


76 


m. 


l; 


/J 


i 


0 


/r/v. 


IT* 


0 HE  HOLE  OUT 

Js 


// 


//I 


y=diam.  ofriv.  +g 


a 


76 


a= I  For  %  rivets;  1$  for 


for  ^rivets 


-M* 
—^ 


With L *  rivets  in  member  deduct  ? rivets  ifb  <  bin  table, 
a   I    "     "      "  "     /     "       b>b"     "          i> 

a  3   //     //     //  //    3    // 


5umof 


5 


b 


II 


is 


ti 


2k 


3/i 


s 


W 


$6 


For  j rivets  take  b^  /ess  than  b  Forjj- . 
"  /" "      "   b^'morethanbfor^ 

O  XT 


STRUCTURAL   TABLES   AND    STANDARDS. 


53 


TABLE  5. 


FOP  GQULKIN6 


r/H 


JHIGKHES5 
OF  PLATE 


a 


B 


c 


D 


a 


B 


C 


D 


{JHVETS 


ff  B  C  D 


ff  B  CD 


geivers 


PS  CD 


/I 


H 


* 


5 
10 


/I 


21 


7" 
10 


2% 


3 


'i 


2k 


3" 


TABLE  6. 
PURLIN  DETAILS. 


8*9  SK)  Channels 
tohaveflanqealso 
attached  to  rafters 


54 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


TABLE   7. 
CARNEGIE  I-BEAMS. 


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STRUCTURAL  TABLES  AND  STANDARDS. 


55 


TABLE   8. 
CARNEGIE  I-BEAMS. 


1 

T1 

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r 

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All  rivets  in  standard  framing  angles  are—  diam. 
Weights  of          ••                 ••              ••      Include  weight  of  shop  rivets  ouly. 
TVhen  beams  frame  opposite  each  other  into  another  beam  with  web  thickness  less 
than-  -A  or  where  beams  of  short  span  lengths  are  loaded  to  their  full  capacity,  {b 
taay  be  necessary  to  use  framing  angles  of  greater  strength  than  the  standards. 
See  table  below  for  .minimum  span  lengths. 

I 

AE'GNT 

SPFT.'N        I       WEIGHT 

SPi?.'N  I 

WEIGHT:^**  IN        J        SVEI-IHTiS^N  JN  i     J      |  *r,GMT  SPAS  "•  i     J      (wEIGH-SPAN  IN 

20 

80.0 
80.0 
65.0 

22.C 
22.  C 

18.0 

: 
IS 

55.0 

15  80.0 
140     '      60.0 
"     42.0 

20.0 
15.5  J 
1LO 

12 

8  iao 

40.O  UL5.  10  25.0    9.0     V    15.0 
3L5    9.0  |  »    210    7.0     6    1225 

5.5 

40 
6.0 

5 
3 

9.75 
7.5 
55 

40 
3-0. 
2.0 

STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


TABLE  9. 
CARNEGIE  CHANNELS. 


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ift 

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9.75 

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4. 

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10.50 

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8.00 

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ii 

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2ii 

i 

8.00 

11.50 

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ift 

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w 

11.50 

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STRUCTURAL  TABLES  AND  STANDARDS. 


TABLE    10. 
CARNEGIE  Z-BARS. 


13 

L 

j 

Ul  dim  t-  n.l 

HIZHE^D 
>D>  In  Ineke 

• 

NOMINAL 

ACTUAL  SIZE 

\VEIGHT 
PER 

AREA 

GAUGE. 

MAX. 

*IVETS 

GAUGE 

rHICXNESS 

NOMINAL 

SIZE. 

FLANGES  4  WEB 

FOOT 

INCHES 

O 

G 

6* 

tf> 

SIZE  * 

i 

2ftx  3     x  2S 

6.7 

1.97 

H- 

1 

| 

a 

••i 

ft 

2f  x  34,  x  2f 

8.4 

2.48 

» 

« 

*• 

A 

| 

2£  x  3    x  2* 

9.7 

2.86 

.» 

•• 

•' 

^ 

1 

s 

ft 
i 

2§       Q  i       24 
2ft  x  3    x  2ft 

11-4 
12.5 

3.36 

•• 

" 

** 

v 

ft 

i 

3 

& 

2*  x  3i  x  21 

14.2 

418 

u 

& 

i 

Sir  x  4     x  3fc 
3i  x  4i  x  3i 
3**  4*  x  3ft 

8.2 
10.3 
12.4 

2.41 
3.03 
3.66 

2 

! 

i 

2 

H*  •«*• 

R 

3i  *  4    x  34 

18J3 

405 

.. 

.. 

„ 

.. 

& 

^ 

3-tx  4ix  3t 

15.8 

4.66 

.. 

.. 

.. 

., 

i 

4 

ft 

34*  4i-x  3& 

17.9 

5^7 

» 

„  . 

.. 

V 

ft 

4 

A 

Ol            *         _    OJL, 

1  Q  Q 

R  S<\ 

.1 

8 

OH  x  4     ^  Oiff 

4.O-W 

O.OD 

8 

& 

3tx4^x  3t 

20.9 

6.14 

.. 

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.. 

M 

i 

i 

34  x  4i  «  3i 

22.9 

6.75 

" 

1 

1 

3*  *  5     x  3t 
3&x  54  x  3& 

11.6 

13.9 

3.40 
4.10 

5 

i 

44 

5 

i 

ft 

3fx  5i-x  31 

16.4 

4fil 

« 

.. 

«« 

» 

ft 

i 

3}  x  5     *  3i 

17.8 

6J25 

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3&x  5&x  3^ 

20^ 

6.94 

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«. 

'• 

» 

ft 

£ 

1 

3|-  *  5*  «  3f 

22.6 

6.64 

*• 

>. 

» 

« 

i 

£ 

ft 

3  r  «  5     x  3* 

2a7 

6.96 

M 

•i 

» 

•• 

ft- 

•f- 

3&  «  5fe  x  a& 

26.0 

7.64 

.. 

M 

.. 

.. 

f 

• 

3i  *  5*  a  3* 

28-3 

8.33 

k 

* 

i 

Si-  x  6     m  3t 

15.6 
18J3 

21.0 

4.59 
5.39 

6.19 

? 

5 

\ 

3 

wH  Sl-fl  coJ 

i 

3*  *  6    «  3J- 

22T7 

6,68 

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,. 

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t 

3^»  6-ix  3& 

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tf 

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3l  *  6*  *  3t 

28JO 

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i 

6 

£ 

34  x  6    »  3i 

29.3 

8.63 

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S2i> 

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- 

,. 

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i 

3«»6«'»3f 

" 

10.17 

* 

STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


TABLE    ii. 

CARNEGIE  ANGLES. 

Weight  in  pounds  per  lineal  foot. 


WEIGHTS  OF  ANGLES 

AH  dimension*  In  Inches 

SIZE 

f 

£ 

f 

•h 

f 

& 

i 
a 

* 

B 
S 

11 
10 

3 

~f 

* 

i 

if 

1 

*& 

*f 

SIZE 

8    x  8 

26.4 

29.5 

32.7 

35.8 

38.9 

42.0 

45.0 

48.0 

51.0 

540 

56.9 

8    ^  8 

Q   *  6 

14.8 

17.2 

19.6 

21.9 

242 

26.5 

28.7 

30.9 

33.1 

35.3 

37.4 

6    ,  6 

• 
5    «  5 

12.3 

14.3 

16.2 

18.1 

20.0 

21.8 

23.6 

25.4 

27.2 

28.9 

30.6 

5    ,5 

4   x  4 

8.2 

9.8 

11.3 

12.8 

143 

15.7 

17.1 

18.5 

19.9 

4    «  4 

3*x  3i 

7.1 

8.5 

9.8 

11.1 

12.3 

13.6 

148 

16.0 

17.1 

3i-x  3i 

3    x  3 

49 

6.1 

7.2 

8.3 

9.4 

10.4 

11.4 

3    .  3 

2£  x  25 

4.5 

5.5 

6.6 

7.6 

8.5 

2ir.  2f 

2*x  2i 

3.1 

4.0 

5.0 

5.9 

6.8 

7.7 

2i«  2i 

2i-x  24 

2.8 

3.7 

4.0 

5.3 

6.1 

6.8 

2f»  2J 

2   »  2 

2.5 

3.2 

4.0 

4.7 

5.3 

2    x  2 

1?-.  11 

2.1 

2.8 

3.4 

4.0 

4.6 

lf»  ii 

1*.  li 

1.2 

L8 

2.4 

2.9 

3.4 

Hx  li 

H-x  i* 

1.0 

1.5 

L9 

2.4 

li-x  «- 

1       X      1 

0.8 

1.2 

1^5 

1        X     1 

size 

1 
s 

& 

1 
T 

& 

3 

S 

7 
26 

1' 

3 

h 

i 

11 
2fi~ 

3 

T 

11 

f 

J£ 

1 

*A 

*1 

SIZE 

7   .  Si 

15,0 

17.0 

19.0 

21.0 

23.0 

249 

26.8 

28,7 

30.5 

32.3 

7    x  3i 

Q   x  4 

• 

12.3 

14.3 

16.2 

iai 

20.0 

21.8 

23.6 

25.4 

272 

28.9 

30.6 

6    «  4 

6   x  Si 

11.7 

13.5 

15.3 

17.1 

iag 

20.6 

22.3 

240 

25.7 

27.3 

28.9 

6   x  3* 

>   *  4 

11.0 

12.8 

145 

16.2 

17.8 

19.5 

21.1 

22.6 

242 

* 
5    «  4 

5   *3) 

8.7 

10.4 

12.0 

13.6 

15.2 

16.8 

18.3 

19.8 

21.3 

227 

5    x  31- 

5    x  3 

8.2 

9.8 

11.3 

12.8 

142 

15.7 

17.1 

18.5 

19.9 

5    «  3 

4  .»3i 

7.7 

9.1 

10.5 

11.9 

13.3 

1-46 

15.9 

17.2 

18.5 

1    *3i 

4  *  3 

7.1 

8.5 

9.8 

11.1 

12.3 

13.6 

148 

16.0 

17.1 

4    *  3 

3ix  3 

6.6 

7.8 

9.1 

10.2 

11.4 

12.5 

13.6 

147 

157 

3i*  3 

Sl.2i 

4.9 

6.1 

13 

8.3 

9.4 

10.4 

U.4 

12.4 

3f  x  2i 

3   »  21 

4.5 

5.5 

6.6 

7.6 

8.5 

9.5 

3    x  2i 

3    x  2 

4.0 

5.0 

5.9 

6.8 

7.7 

3  x  a 

2V*  2 

2.8 

3.7 

4.5 

5.3 

6-1 

6.8 

2i»  2 

SIZB 

£ 

& 

1 
~4 

& 

JL 

y 

£ 

i 
IT 

& 

-f 

& 

* 

* 

f 

# 

1 

J& 

4 

SIZE 

Angles  marked    *  are  special 

STRUCTURAL   TABLES    AND   STANDARDS. 


59 


TABLE    12. 

CARNEGIE  ANGLES. 

Areas  in   Square  Inches. 


ANGLES 

Area  In  square  Indies. 

SIZE 

f 

3 

13 

I" 

s 
IS 

f 

i* 

i 

& 

f- 

£ 

-f 

ft 

i 

8 

1 

lh 

*£ 

SIZE 

8   «  8 

7.75 

8.68 

9.61 

10.53 

1144 

12.34 

13.23 

14*2 

15.00 

15.87 

16.73 

8   «  8 

6,6 

436 

5.06 

5.75 

6.43 

7.11 

7.78 

8.44 

9.09 

9.74 

10.37 

11.00 

6   «  6 

5    «  5 

3.61 

4,18 

4,75 

5.31 

5.86 

6.42 

6.94 

7.46 

7.99 

8.50 

9.00 

5    .  5 

4   .4 

2.40 

2.86 

3.31 

3.75 

418 

4.61 

5.03 

5.44 

5.84 

4   x  4 

3V»  3i 

2.09 

2.48 

2.87 

3.25 

3.62 

3.98 

434 

4.69 

5.03 

3*«3i 

3   x  3 

1.44 

1.78 

2.11 

2.43 

2,75 

3.06 

3.36 

3    x  3 

*2f*  21 

1.31 

1.62 

1.92 

2.22 

2.50 

2J«  2? 

2V*2i 

0.901 

1.19 

1.47 

1.73 

2,00 

2.25 

2|-«  2i 

2'*  «  2} 

0.81 

1.06 

1.31 

1.55 

1.78 

2.00 

*2i  «  2i 

2    >  2 

0.72 

0.94 

1.15 

1.36 

1.56 

2   x  2 

11-  »  1! 

0.62 

0.81 

1.00 

1.17 

1.30 

If*  1} 

Ifr.  1* 

0.36 

0.53 

0.69 

0.84 

0.99 

li»  li 

1*  »  U 

0.30 

0.43 

0.56 

0.69 

If.  li 

l   .  1 

0.24 

0.34 

0.44 

1    »  1 

size 

I" 

A 

£• 

& 

£ 

Is 

JL 

i 

9 
1G 

f 

M. 

3.0 

f 

8 

f- 

8 

1 

& 

/f 

SIZE 

7    .  3^ 

4,40 

5.00 

5.59 

6.17 

6.75 

7.31 

7.87 

8.42 

8.07 

9.50 

7   «  3i 

6    »  4 

3.61 

4.18 

475 

5.31 

5.86 

6.41 

6.94 

7.47 

7.99 

8.50 

9.00 

6    »  4 

6    «  34 

3.42 

3.97 

450 

5.03 

5.55 

6.06 

6.56 

7.06 

7.55 

8-03 

8.50 

6    .  3^ 

5    »  4 

3.23 

3.75 

425 

475 

5.23 

5.72 

6.19 

6.65 

7.11 

*5   ,4 

5    .  3| 

2.56 

3.05 

3.53 

4.00 

4.47 

492 

5.37 

5.81 

6.25 

6.67 

5    .  3j 

5    .  3 

2.40 

2.86 

3.31 

3.75 

418 

4.61 

5.03 

5.44 

5.84 

5   M  3 

4    ,  3* 

2.25 

2.67 

3.09 

3.50 

3.90 

430 

468 

5.06 

5.43 

4    <  3i 

4    »  3 

2,09 

2.48 

2.87 

3.25 

3.62 

3.98 

434 

469 

5.03 

4   >  3 

3*i  3 

193 

2.30 

2.65 

3.00 

3.34 

3.67 

400 

431 

462 

3^x  3 

3^x  2| 

1.44 

L78 

2.11 

2.43 

2.75 

3.06 

3.36 

3.65 

3i-«  2^ 

3   »  2i 

L31 

L62 

1.92 

2.22 

2.50 

2.78 

3    x  2* 

3    x  2 

119 

147. 

1.73 

2.00 

2.25 

3    «  2 

2*»  2 

0.81 

1.06 

LSI 

1.5-5 

1,78 

2.00 

2i-«  2 

SIZE 

JL 

i 

h 

i 

* 

3 

a 

h 

J_ 
s 

£ 

5 

a 

11 

1G 

f 

12. 

1G 

7 

I 

13. 
Hi 

1 

lh 

# 

SIZE 

Angles  marked  *  are  speciaL 

6o 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND   DESIGNS. 


TABLE    13. 
UPSETS  FOR  ROUND  AND  SQUARE  BARS. 


ROUND     (~)     BARS 

SQUARE       |       [       BARS 

ROUHO 

UPSET 

UPSET 

SQUARE 

MAM. 

A*  (A 

OIAM. 

LENGTH 

ADO 

AREA 

AT  ROOT 

Excess 

AREA 

EXCEtl 

AREA 
AT  ROOT 

ADO 

LENGTH 

O.AM. 

MI* 

0)  AM. 

INCHES 

.*m.. 

INCHC* 

INCHES 

INCHES 

M.,N.. 

% 

% 

Jfl.lNS. 

mCME, 

INCME» 

,NCH" 

W*» 

INCHES 

t 
T 

0.307 

T 

4 

4i 

0.420 

36.8 

a 

» 

£ 

0.442 

1 

4 

3} 

0.550 

24.4 

206 

0.694 

34 

4 

1} 

0.563 

3 

t 

i 

0.601 

u 

4 

6 

0.891 

48.3 

16.3 

0.891 

4 

4 

M 

0.766 

t 

8 

1 

0.785 

11 

4 

4^ 

1.057 

34.7 

29.5 

1.295 

4 

4 

ti 

1.000 

1 

11 

0.994 

li 

4 

3; 

1.295 

30.3 

19.7 

L515 

4i 

4i 

ii 

1.266 

11 

li 

1.227 

If 

4i 

3? 

1.515 

23.5 

3L1 

2.049 

4i 

41 

1; 

1.563 

11 

11 

1.485 

If 

4* 

31 

L744 

17.4 

2L7 

2.302 

4| 

5 

2 

1.891 

n 

11 

1.767 

2 

5 

4T 

2.302 

30.3 

34.0 

3.023 

4f 

5 

2i 

2.2&0 

li 

H 

2.074 

2r 

5 

4; 

2.651 

27.8 

29.6 

3.410 

41 

5i 

2; 

2.641 

IT 

H 

2.405 

27 

5 

4 

ao23 

25.7 

21.3 

3.716 

4  i 

51 

21 

3.063 

lj 

il 

2.761 

2* 

«i 

4i 

3.410 

23.9 

31.4 

4.619 

Si 

6 

2f 

3.516 

IT 

2 

3.142 

2? 

51 

3* 

3.716 

18.3 

27.7 

5.107 

4! 

6 

27 

4.000 

2 

2i 

3.547 

25 

5i 

3| 

4.155 

17.1 

20.2 

5.430 

4} 

6 

3 

4.516 

21 

21 

3.976 

2J 

6 

4* 

5.107 

28.5 

28.6 

6.510 

5^ 

ei 

Si- 

5.063 

21 

21- 

4.430 

3 

6 

4r 

5.430 

22.6 

33.8 

7.548 

6| 

7 

3i 

5.641 

.21- 

21- 

4.909 

3* 

64 

4f 

5.957 

2L3 

30.7 

8.170 

6r 

8 

8* 

6.250 

21 

21 

5.412 

3^ 

6i 

4; 

6.510 

20.3 

35.0 

9.305 

6f 

8 

3^ 

6.891 

21 

& 

5.940 

31 

7 

47 

7.088 

19.3 

32.1 

9994 

6 

"8 

4 

7.563 

21 

21 

6.492 

3f 

8 

5^- 

8.170 

25.9 

37.0 

11.329 

8 

9 

4r 

8.266 

27 

3 

7.069 

3r 

8 

5i- 

8.641 

22.2 

417 

12.753 

?* 

9 

4i 

9.000 

3 

31 

7.670 

37 

8 

5j 

9.305 

2L3 

31 

31 

8.296 

4 

8 

4T 

9.994 

J0.7 

31 

3i 

9.621 

4* 

9 

5; 

11.329 

17.7 

3^ 

31 

11.045 

4; 

9 

47 

12.753 

15.5 

31 

STRUCTURAL   TABLES   AND   STANDARDS. 


61 


TABLE    14. 

CLEVISES.    AMERICAN  BRIDGE  COMPANY  STANDARDS. 
All  Dimensions   in  Inches. 


DIAM.OF 

CLEVIS 

D 


MAX,  PIH 

p 


FORK 

F 


NUT 
H 


WIDTH 
IT 


THICKNESS 

r 


OIAM.OF 
CLEVIS 

m 


Tal>le  giving  diameter  of  Clevis  for  given  rod  and  pin. 


Clevises  above  and  to  right  of  beavy  zigzag  line,  may  be  used  with  forks  straight. 
Clevises  below  and  to  left  of  same  line,  should  have  forks  closed  in  until  pin  is  not 
overstrained. 


62 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS, 


TABLE    15. 

SLEEVE  NUTS  AND  TURNBUCKLES     AMERICAN  BRIDGE  COMPANY  STANDARDS. 
All  Dimensions   in  Inches. 


U    •**    >! 

>Q 

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Manufactured   by   the 
Cleveland  City  Forge  <t   Iron  Company, 
Cleveland,  Ohio. 

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LENGTH 
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LENGTH 
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104 
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14 
15 
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13 
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22 
23 

27 

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28 
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Bf 

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31 

2 

3 

« 

13 

65 

« 

3s- 

ft 

1 

40 
45 
47 
52 

65 

Is 

4 
5 

8; 

4s 

18 

6 

5 

4 

5 

14 

6; 

8 

47 

If. 

55 
65 
75 

la 

5 

M 

18 

6 

< 

STRUCTURAL    TABLES    AND    STANDARDS. 


TABLE    16. 

LOOP  BARS.    AMERICAN  BRIDGE  COMPANY  STANDARDS. 
All  Dimensions   in  Inches. 


Ssas   ssss  515$ 


oJc^Soi        CD  co  co  co        ^  «°  <0  t-     c* 


S     SS8S     8SSS     SSSS   5 


ssss  s 


-       -      n  •  -n  _<,  o»  -(,_!«-(» 

CO't          ^OCOt-          OTO>Ort         OCOTiO       CO 
00          05  (N  C3  c-J          01  05  C3  CO         PJCOOCO       03 


P|.f|*»l*       «|«.I.-H,-)™       *.-I»-I» 

sssa   ^ssg   5ss 


c    c-  D  a»       o^o»co     ^ 
owwoq       SocoS     TO 


o->-cfl     eo 

C3COC3CO       O 


^.          ^  -.  W  Cl          CM   0)  05  01 


OJC^CQC^        CQ  co  co  co      co 


c«  01  co  co     co 


^rocot-       coa>o^     "-1 

O1OJOJO1          (NOflCOCO        CO 


O   CO          C-.  00  ®  O       -^ 
OJ    OJ          CQ   Ol  03   CO        CO 


coc-ooco       a>o-*c<> 


<3>O-*C<>          COTJ«OO          C--000&O       ^ 

^ojojoa        ojoiooj       cicjojco     co 


8£8c1     § 


Co  05  c    ^ 


64 


STRUCTURAL   DRAWINGS,  ESTIMATES   AND  DESIGNS. 


TABLE   17. 
EYE  BARS.    AMERICAN  BRIDGE  COMPANY  STANDARDS. 


© 

Ordinary 

f 

<, 

Adjustable 
^ 

N- 
i 

) 

1 

lil!SL> 

X"^ 

i 

L 

Mln.  Length  C.  to  end     O*  O."  preferably  7  '  o" 

WIDTH 
OF 
BAR 

THICKNESS 
OF  BAR 

HEAD 

SCREW  END 

THICKNISS 
OF  BAR 

VKIDTH 
OF 
BAR 

OIAM. 

PIN. 

FOR  HEAD 

ADD'L  MATCRIAL 

dA-. 

UNOTH 

INS. 

INS. 

INS. 

INS. 

FT.i.NS. 

FT.   A  INS. 

m* 

,NS. 

INS. 

INS. 

2 

.8 

4i- 

u- 

0-  7i 

'0-  7 

2 

5  ' 

• 

2 

5* 

2? 

1-  Oj 

»i 

| 

65 

2y 

0-  9i 

1-    1 

a* 

5 

1!  -  U 

2i 

6? 

3i 

1-  li 

3 

.i 

7 

3 

1 

-  3 

-  5 

2r 

6* 

1  tolrS 

3 

" 

8 

4 

1 

-  6 

-  5 

2  f 

6 

11  to  n 

4 

| 

9i 

47 

1 

-  8 

-  8 

3 

6 

'     1  to  11 

4: 

" 

lOi 

5T 

1 

-10 

-  8 

3  r 

6i 

lr«  to  *i 

5 

i 

llf 

5 

1 

-  9 

-  9 

3. 

6i 

1  to  1^ 

5 

1 

12i 

6. 

2 

-  1 

-  9 

s* 

7 

11  tolj 

6 

1 

13i 

5i 

1 

-11 

-11 

3f 

8 

1J  to  1^ 

G 

1 

14* 

6i 

2 

-   2 

-11 

4 

8 

It  101} 

7 

i 

16 

6^- 

2 

-  3 

2-  3 

4* 

9 

U  ««  1A 

7 

* 

17 

7f 

2 

-  8 

2-  3 

4? 

9 

1J  to  1J 

8 

i 

17 

6i- 

2 

-   3 

8 

HI 

18 

7-i 

2-   6 

li 

18r 

8 

2 

-10 

I* 

19y 

7r 

2-  6 

9 

9 

» 

2lT 

9i- 

3 

-  1 

li 

22 

9 

2 

-  11 

10 

10 

« 

23 

10 

3-  3 

12 

12 

JSote:  Eye  bars  are  hydraulic  lorged,  and  are  guaranteed  to  develop  the  fall  strength  ot  the  bar, 
under  conditions  gbrenta  the  above  table,  when  tested  to  dosti  uctlon. 

STRUCTURAL   TABLES    AND   STANDARDS. 

TABLE   18. 
BRIDGE  PINS  WITH  LOMAS  NUTS. 


65 


ET 
PIN. 


PIN. 


Screw. 


2/2 


X 


STANDARD  DIMENSIONS. 


6  Threads  per  Inch. 


NUT. 


iam.  of 
gh  Hole. 


3X 


4rV 


5A 
5A 


Wei 
PO 


2-5 
2-5 
2-5 
2-5 
3-0 
3-0 
3-0 


3/2 


4X 

4X 

5 


3A 
3A 
3A 
3lt 
3H 
4A 
4T5ff 
4A 


5 
5 
5* 


5-5 

5-5 
7.0 
7.0 
7.0 
8-5 
8-5 

II.O 
1  1.0 
II.O 


s* 

4 

4X 

4X 

4X 

5 

5X 


6X 


7X 
8 


5 
5 

5X 

5/2 
5/2 

6 
6 


5lt 


8X 
8X 
9 
9 


I2.O 
12.0 
13-5 
13-5 
13-5 
17.0 
17.0 


7 

7/2 

1% 
8 


Note. — To  obtajn  grip  "  G "  add  &"    for  each  bar,  together  with  amount 
given  in  table. 


66 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE   19. 

STANDARD  COTTER   PINS. 

All  Dimensions  in  Inches. 


f 


DlAM. 
OF 

PIN. 
P 


PIN. 


i.U 

Iff 


fV  X 


X  A 
XA 


A  X 
TV  X  A 


X5 
"31 

XA 

X7 
TI 


HEAD. 


COTTER. 


4 


t 
\* 


£ 
j| 


ADD  TO  GRIP* 


i* 


1/8 
13/8 


I# 


DlAM. 

OF 

PIN. 
P 


Note. — Use  pins  with  lomas  nuts,  in  preference  to  cotter  pins,  whenever 
possible. 


STRUCTURAL  TABLES  AND  STANDARDS. 


67 


TABLE  20. 

STANDARD  CAST   O.   G.   WASHERS. 
All  Dimensions  in  Inches. 

71 


?  for  sizes  notqiren  befow. 


DIAMETER  OF 
BOLT  d. 


WEIGHT  IN 
POUNDS. 


2/S 
2/2 


IT\ 

lT57T 


68 


STRUCTURAL   DRAWINGS,   ESTIMATES    AND  DESIGNS. 


TABLE    21. 

MAXIMUM  ALLOWABLE'  BENDING  MOMENTS  IN  PINS  FOR  VARIOUS  FIBER  STRESSES. 


PIN 

MOMENTS  IN  INCH  POUNDS  FOR  FIBRE  STRESSES  PER  SQ.  IN.  OF 

DIAM. 

INCHES 

AREA 

15,000 

18,000 

20,000 

22,000 

25,000 

1 

0.785 

1470 

1770 

1960 

2160 

2450 

H 

1.227 

2880 

3450 

3830 

4220 

4790 

if 

1.767 

4970 

5960 

6630 

7290 

8280 

if 

2.405 

7890 

9470 

10500 

11570 

13200 

2 

3.142 

11800 

14100 

15700 

17280 

19600 

21 

3.976 

16800 

20100 

22400 

24600 

28000 

2* 

4.909 

23000 

27600 

30700 

33700 

38400 

2| 

5.940 

30600 

36800 

40800 

44900 

51000 

3 

7.069 

39800 

47700 

53000 

58300 

66300 

31 

8.296 

50600 

60700 

67400 

74100 

84300 

3 

9.621 

63100 

75800 

84200 

92600 

105200 

3f 

11.045 

77700 

93200 

103500 

113900 

129400 

4 

12.566 

94200 

113100 

125700 

138200 

157100 

41 

14.186 

113000 

135700 

150700 

165800 

188400 

15.904 

134200 

161000 

178900 

196800 

223700 

4f 

17.721 

157800 

189400 

210400 

231500 

263000 

5 

19.635 

184100 

220900 

245400 

270000 

306800 

51 

21.648 

213100 

255700 

284100 

312500 

355200 

23.758 

245000 

294000 

326700 

359300 

408300 

51 

25.967 

280000 

335900 

373300 

410600 

466600 

6 

28.274 

318100 

381700 

424100 

466500 

530200 

61 

30.680 

359500 

431400 

479400 

527300 

599200 

•f 

33.183 

404400 

485300 

539200 

593100 

674000 

61 

35.785 

452900 

543500 

603900 

664200 

754800 

1 

38.485 

505100 

606100 

673500 

740800 

841900 

71 

41.282 

561200 

673400 

748200 

823000 

935300 

ll 

44.179 

621300 

745500 

828400 

911200 

1035400 

1\ 

47.173 

685500 

822600 

914000 

1005300 

1142500 

8 

50.265 

754000 

904800 

1005300 

1105800 

1256600 

81 

53.456 

826900 

992300 

1102500 

1212800 

1378200 

si 

56.745 

904400 

1085200 

1205800 

1326400 

1507300 

8-1 

60.132 

986500 

1183800 

1315400 

1446900 

1644200 

STRUCTURAL    TABLES    AND    STANDARDS. 


69 


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STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


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STRUCTURAL   TABLES   AND    STANDARDS. 


TABLE  23. 

TABLE  OF  AREAS  IN  SQUARE  INCHES,  TO  BE  DEDUCTED  FROM  RIVETED  PLATES  OR 
SHAPES  TO  OBTAIN  NET  AREAS. 


88  PLATES! 
4CHE8. 

SIZE  OF  HOLE.     INCHES. 

ITHICKNE 
IN  II 

* 

A 

1 

X* 

* 

T'* 

f 

tt 

1 

it 

* 

15 

1 

IA 

i 

.06 

.08 

,09    .11 

.13 

.14 

.16 

.17 

.19 

.20 

.22 

.23 

.25 

.27 

A 

.08 

.10 

.12    .14 

.16 

.18 

.20 

.21 

.23 

.25 

.27 

.29 

.31 

.33 

1 

.09 

.12 

.14 

.16 

.19 

.21 

.23 

.26 

.28 

.30 

.33 

.35 

.38 

.40 

.11 

.14 

.16 

.19 

.22 

.25 

.27 

.30 

.33 

.36 

.38 

.41 

.44 

.46 

^ 

.13 

.16 

.19 

.22 

.25 

.28 

.31 

.34 

.38 

.41 

.44 

.47 

.50 

.53 

& 

.14 

.18 

.21 

.25 

.28 

.32 

.35 

.39 

.42 

.46 

.49 

.53 

.56 

.60 

1 

.16 

.20 

.23 

.27 

.31 

.35 

.39 

.43 

.47 

.51 

.55 

.59 

.63 

.66 

H 

.17 

.21 

.26 

.30 

.34 

.39 

.43 

.47 

.52 

.56 

.60 

.64 

.69 

.73 

t 

.19 

.23 

.28 

.33 

.38 

.42 

.47 

.52 

.56 

.61 

.66 

.70 

.75 

.80 

« 

.20 

.25 

.30    .36 

.41 

.46 

.51 

.56 

.61 

.66 

.71 

.76 

.81 

.86 

1 

.22 

.27 

.33    .38 

.44 

.49 

.55 

.60 

.66      .71 

.77 

.82 

.88 

.93 

it 

.23 

.29 

.35 

.41 

.47 

.53 

.59 

.64 

.70 

.76 

.82 

.88 

.94 

1.00 

1 

.25 

.31 

.38 

.44 

.50 

.56 

.63 

.69 

.75 

.81 

.88 

.94 

1.00 

1.06 

IA 

.27 

.33 

.40 

.46 

.53 

.60 

.66 

.73 

.80 

.86 

.93 

1.00 

1.06 

1.13 

H 

.28 

.35 

.42 

.49 

.56 

.63 

.70 

.77 

.84 

.91 

.98 

1.05    1.13 

1.20 

.30 

.37 

.45 

.52 

.59 

.67 

.74 

.82 

.89 

.96 

1.04 

1.11 

1.19 

1.26 

H 

.31 

.39 

.47 

.55 

•63 

.70 

.78 

.86 

.94 

1.02 

1.09 

1.17 

1.25 

1.33 

.33 

.41 

.49 

.57 

.66      .74 

.82 

.90 

.98    1.07  i  1.15 

1.23 

1.31 

1.39 

1? 

.34 

.43 

.52    .60 

.69 

.77 

.86 

.95 

1.03 

1.12    1.20 

1.29 

1.38 

1.46 

.36 

.45 

.54 

.63 

.72 

.81 

.90 

.99 

1.08 

1.17 

1.26 

1.35 

1.44 

1.53 

H 

.38 

.47 

.56 

.66 

.75 

.84 

.94 

.03 

1.13 

1.22 

1.31 

1.41 

1.50 

1.59 

IA 

.39 

.49 

.59 

.68 

.78 

.88 

.98 

.07 

1.17 

1.27 

1.37 

1.46 

1.56 

1.66 

if 

.41 

.51 

.61 

.71 

.81 

.91 

1.02 

.12 

1.22 

1.32 

1.42 

1.52 

1.63 

1.73 

.42 

.53 

.63 

.74 

.84 

.95 

1.05 

.16 

1.27 

1.37 

1.47 

1.58 

1.69 

1.79 

l|g 

.44 

.55 

.66 

.77 

.88 

.98 

1.09 

.20 

1.31 

1.42 

1.53 

1.64 

1.75 

1.86 

.45 

.57    .68 

.79 

.91 

1.02 

1.13 

.25 

1.36 

1.47 

1.59 

1.70 

1.81 

1.93 

H 

.47 

.59 

.70 

.82 

.94 

1.05 

1.17 

.29 

1.41 

1.52 

1.64 

1.76 

1.88 

1.99 

.48 

.61 

.73 

.85 

.97     1.09 

1.21 

.33 

1.45 

1.57    1.70 

1.82 

1.94    2.06 

2T6 

.50|  .63    .75    .88 

1.00    1.13 

1.25      .38 

1.50    1.63    1.75 

1.88    2.00    2.13 

In  calculating  the  net  area  add  ^  inch  to  diameter  of  rivet  before  entering 
the  table. 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE  24. 
AMERICAN   BRIDGE   Co.'s   STANDARD   BUCKLE   PLATES. 


V 

Size  of  Buckle 

Rad.  of  Buckle 

el 

o 

Size  of  Buckle 

Rad.  of  Buckle 

8 

rt 

in  Feet  and 

9  « 

in  Feet  and 

c  ^ 
3  u 

| 

in  Feet  and 

.2  <«' 

in  Feet  and 

E  ^14 

s  u 

5 

Inches. 

«j§ 

Inches. 

.§« 

E 

Inches. 

8-S 

Inches. 

M 

•8 

31 

IS 

•o 

'&£ 

jh 

g 

Length. 

Width. 

Length. 

Width. 

3d 

d 

Length. 

Width. 

Length. 

Width. 

S  d 

fe 

L 

US 

R 

L 

w 

£ 

fc 

L 

W 

R 

L 

W 

8 

i 

3-" 

4-6 

3% 

6-8 

8-9 

7 

20 

2-9 

2-6 

*X 

4-7 

3-10 

10 

2 

4-6 

3-u 

3/2 

8-9 

6-8 

6 

21 

2-6 

2-6 

*y* 

3-10 

3-10 

10 

3 

3-i  i 

3-6 

3 

7-9 

6-3 

7 

22 

3-5 

3-6 

3 

5-i  i 

6-3 

8 

4 

3-6 

3-i  i 

3 

6-3 

7-9 

8 

23 

3-6 

3-5 

3 

6-3 

5-" 

8 

5 

3-9 

3-9 

3 

7-i 

7-i 

8 

24 

3-6 

3-9 

3 

6-3 

7-i 

8 

6 

3-i 

3-9 

3 

4-10 

7-i 

9 

25 

3-9 

3-6 

3 

7-i 

6-3 

8 

7 

3-9 

3-i 

3 

7-i 

4-10 

8 

26 

3-1 

3-2 

3 

4-10 

5-i 

9 

8 

3-8 

3-8 

2 

10-2 

10-2 

8 

27 

3-2 

3-i 

3 

5-i 

4-10 

9 

9 

2-8 

3-8 

2 

5-5 

10-2 

10 

28 

3-i 

3-o 

3 

4-10 

4-7 

9 

10 

3-8 

2-8 

2 

10-2 

5-5 

8 

29 

3-o 

3-i 

3 

4-7 

4-10 

9 

ii 

2-2 

3-8 

2 

3-7 

10-2 

10 

3° 

2-0 

2-6 

2/2 

2-6 

3-10 

10 

12 

3-8 

2-2 

2 

10-2 

3-7 

8 

3i 

2-6 

2-O 

2/2 

3-10 

2-6 

15 

!3 

3-o 

3-o 

2 

6-10 

6-10 

9 

32 

3-6 

5-6 

3% 

5-4 

13-1 

5 

H 

2-9 

2-9 

3 

3-10 

3-10 

10 

33 

5-6 

3-6 

3/2 

I3-I 

5-4 

i 

19 

2-6 

2-9 

2/2 

3-10 

4-7 

10 

34 

4-0 

4-0 

3 

8-1 

8-1 

7 

Plates  are  made  £ 


|//  Or  ^  thick. 


Buckles  of  different  sizes  should  not  be  used  in  the  same  plate. 
Rivets  generally  |x/  or  |x/  diameter. 


STRUCTURAL    TABLES    AND    STANDARDS. 


73 


TABLE  25. 
TYPICAL   HAND   CRANES. 


Capacity  in 
Tons. 

Span, 
Ft. 

Wheel 
Base. 

Maximnm 
Wheel 
Load,  Lbs. 

Vertical 
Clearance. 

Side 
Clearance. 

Weight  of  Rails,  Lbs. 
per  Yard  for 

I  Beams. 

Plate 
Girders. 

3° 

4'-o" 

3,  ico 

4/-o" 

77/ 

30 

30 

2 

50 

5'-o" 

4,000 

4'-o" 

7" 

30 

30 

30 

4'-o" 

5,400 

4'-6" 

8^ 

30 

30 

4 

50 

5'-o" 

6,500 

4^-6^ 

8^ 

30 

30 

30 

G'-o" 

8,000 

5/-o" 

9// 

30 

35 

50 

7/_o// 

9,200 

5'_o// 

9// 

30 

35 

30 

G^o" 

10,500 

5/-</' 

10" 

35 

40 

50 

7/-o// 

II,  800 

5x-ox/ 

IO"* 

35 

40 

T<"i 

33 

Jf'-o" 

13,000 

5/^// 

IC/^ 

40 

40 

jo 

53 

S'-o" 

14,400 

$'-v" 

IC/' 

40 

40 

ifi 

30 

7/_o// 

20,700 

*>'-&' 

10^ 

45 

45 

1U 

50 

S'-o" 

22,300 

$'-6" 

10" 

45 

45 

/%>-* 

30 

7'-o" 

26,000 

5/-6// 

10" 

50 

So 

i-O 

50 

8/-o// 

23,000 

5/_6^ 

10" 

5o 

5o 

30 

y/.O// 

32»3co 

6'-o" 

12" 

5o 

55 

2J 

50 

8/_o//        35,000 

6/-o// 

12" 

So 

55 

74 


STRUCTURAL   DRAWINGS,   ESTIMATES   AND   DESIGNS. 


TABLE  26. 
TYPICAL  ELECTRIC  TRAVELING  CRANES. 


Capacity, 
Tons. 

Span, 
Ft. 

Wheel 
Base. 

Maximum 
Wheel 
Load,  Lbs. 

Total 
Weight  of 
Crane, 
Lbs. 

Side 
Clearance. 

Vertical 
Clearance. 

Weight  of  Rail, 
Lbs.  per  Yard,  for 

Plate 
Girders. 

I'Ceams. 

3} 

1030 

6'   9" 

9,600 

16,700 

9¥f 

4'  10" 

40 

40 

3* 

3^ 

£ 

6'  II" 

10'    o" 

10,400 
12,600 

19,200 
27,700 

9¥' 

vf\ 

4'  11" 
5'   3" 

40 
40 

4° 
40 

5 

to  30 

8'  o" 

II,  600 

19,500 

10" 

6'   o" 

40 

40 

5 

40 

8'   6" 

1  2,  CCO 

22,400 

10" 

6'   o" 

40 

43 

5 

60 

10'     0" 

J5>500 

3l>3°° 

10" 

6'   o" 

40 

^0 

7} 

to  30 

8'  6" 

14,900 

22,300 

10" 

6'   o" 

40 

40 

7} 

40 

•  8'   8" 

l6,2OO 

24,900 

10" 

6'   c" 

40 

40 

il 

60 

xo'   o" 

19,100 

34,100 

10" 

6'   o" 

40 

40 

10 

to  30 

8'  6" 

l8,500 

23,500 

10" 

6'   o" 

AS 

40 

10 

40 

8'   S" 

19,800 

28,400 

10" 

6'   c" 

A3 

40 

JO 

Co 

10'   o" 

22,700 

37,800 

10" 

6'   c" 

45 

40 

15 

to  30 

9'   6" 

25,700 

29,600 

12" 

6'    7" 

5o 

50 

15 

40 

9'    I" 

27,100 

33,9oo 

12" 

6'   9" 

53 

50 

15 

60 

10'     0" 

29,900 

44,000 

12" 

6'  ii" 

5=> 

5° 

20 

to  30 

9'   6" 

32,300 

34,200 

12" 

7'    i" 

,55 

5o 

2O 

40 

9'   6" 

34,300 

38,800 

zaX'f 

7'   3" 

55 

53 

20 

60 

10'     0" 

38,300 

50,700 

13" 

7'   6" 

55 

50 

25 

to  40 

9'   o" 

40,200 

44,500 

13" 

7'    7" 

60 

5o 

25 

60 

10'   o" 

45,300 

59.500 

13" 

8'   o" 

60 

5° 

30 

to  40 

9'   8" 

46,200 

51,100 

I3" 

8'    c" 

70 

60 

3° 

60 

10'   4" 

52,200 

68,000 

14" 

8'    6'' 

73 

60 

40 

to  40 

10'   8" 

6l,000 

69,300 

1  6" 

8'   9" 

80 

60 

40 

60 

11^    2" 

68,600 

87,000 

16" 

9'    i" 

80 

60 

50 

to  40 

II'    2" 

74,000 

77,  ico 

16" 

9'   5" 

ICO 

Co 

50 

60 

ii'   6" 

86,000 

98,500 

16" 

9'   5" 

ICO 

60 

STRUCTURAL   TABLES    AND   STANDARDS. 


75 


TABLE   27. 
TABLE  FOR  RIVET  SPACING. 


8 

PITCH  IN  INCHES 

i 

ft 

li 

Ik 

If 

^ 

n 

Jt 

*l 

2 

2i 

%± 

2% 

24 

** 

21 

*l 

i 

1 

i 

2 

-2; 

•  2i 

-as 

-  3 

•  3i 

-3J 

-31 

-4 

-4J 

-4i 

-4; 

-5 

-5i 

-54 

-5! 

2 

3 

-  3i 

-  31 

-41 

•  4j 

•41 

-5-i 

-5| 

-6 

-6J 

-6£ 

-7i 

•74 

•71 

-8i 

-8! 

3 

4 

-41 

-  5 

-5i 

-6 

•61 

'  -7 

-7i 

•8 

-8i 

-0 

-ej 

-10 

-104 

-11 

-11* 

4 

5 

•SJ 

-6i 

-6? 

•7} 

-8J 

-8| 

-9| 

-10 

-10{ 

-lli 

-115 

1-Oi 

1-  U 

1-  U 

1-2J 

5 

6 

-  6! 

-TJ 

•84 

-9 

-9! 

-104 

-Hi 

1-0 

1-03 

1-H 

1-  2i 

1-3 

1-33 

1-4. 

l-5i 

6 

7 

•  7* 

-8J 

-9| 

•10} 

-Ill 

1-Oi 

1-  U 

1-2 

1-2} 

1-3J 

1-4| 

1-5} 

1-62 

1-7! 

l-8i 

7 

8. 

-9 

-10 

-11 

1-0 

1-  1 

1-2 

1-3 

1-4 

1-5 

1-6 

1-7 

1-8 

1-0 

1-10 

1-11 

8 

9 

•KH 

•iii 

1-03 

1-  H 

1-2| 

1-3J 

1-41 

1-6 

l-7i 

1-8^ 

1-01 

1-104 

1-11^ 

2-0! 

2-  15 

» 

10 

-115 

i  oj 

1-  1] 

1-3 

1-4J 

1-5} 

1-6J 

1-8 

1-Oi 

1-lOi 

1-11! 

2-  1 

2-21 

2-31 

2-4| 

10 

11 

1-0! 

i-  n 

1-3* 

l-4i 

1-5J 

l-7i 

1-8| 

1-10 

1-11J 

2-  01 

2-  2| 

2-31 

a-  45 

2-6* 

2-7| 

11 

12 

1-  li 

1-3 

1-4} 

1-6 

l-7i 

1-0 

1-10J 

2-0 

2-H 

2-3 

2-4^ 

2-6 

2-74 

2-0 

2-104 

12 

13 

1-21 

1-4; 

1-5J 

1-74 

i-et 

1-10! 

2-0! 

2-2 

2-3! 

2-5i 

2-  6i 

2-8,1 

2-10* 

2-11! 

3-  11 

13 

14 

l-3i 

1-6* 

i-7i 

1-0 

1-10J 

2-Oi 

a-  aj 

2-4 

2-5| 

a-  7i 

2-Oi 

2-11 

3-0! 

3-2i 

3-41 

14 

15 

l-4i 

1-62 

1-81 

1-10J 

2-0B^ 

2-2i 

2-4i 

2-6 

2-7J 

2-0! 

2-1  If 

3-  11 

3-31 

3-5i 

3-7i 

15 

16 

1-6 

1-8 

1-10 

2-0 

2-2 

2-4 

2-6 

2-8 

2-10 

3-0 

3-2 

3-4 

3-6 

3-8 

3-10 

16 

17 

1-7* 

1-Oi 

1-111 

2-  « 

2-3| 

2-51 

2-7i 

2-10 

3-0.1 

3-2* 

3-4| 

3-64 

3-8| 

3-10! 

4-OJ 

17 

18 

l-8i 

1-10J 

2-01 

2-3 

2-51 

2-7i 

2-01 

3-0 

3-2i 

3-41 

3-6! 

3-^ 

3-lli 

4-14 

4-3! 

18 

19 

IQ3 

11  1  3 

20  » 

2-  41 

2-e; 

2-9] 

2-111 

3-3 

3-4| 

3-6! 

3-0.1 

3-114 

4-15 

4-4J 

4-61 

19 

20 

L-iOi 

2-  1 

2-  34 

2-  6 

2-8* 

2-11 

3-  li 

3-4 

3-6i 

3-0 

3-1  li 

4-2 

4-4* 

4-7 

4-04 

20 

21 

IH1| 

2-  2r 

2-  4| 

2-74 

2-10i 

3-OJ 

3-3| 

3-6 

3-8| 

3-m 

4-  1J 

4-44 

4-7i 

4-9! 

5-01 

21 

22 

2-OJ 

2-  31 

2-6! 

2-0 

2-1  1J 

3-2J 

3-5i 

3-8 

3-10'; 

4-  li 

4-4J 

4-7 

4-9J 

5-OJ 

5-3! 

22 

23 

2-  1J 

2-4| 

2-7| 

2-10J 

3-  1| 

3-4i 

3-7J 

3-10 

4-01 

4-31 

4-6! 

4-ej 

5-01 

5-3! 

5-6* 

23 

24 

2-3 

2-6 

2-0 

3-0 

3-3 

3-6 

3-9 

4-0 

4-3 

4-6 

4-0 

5-0 

5-3 

5-6 

5-0 

24 

25 

2-4J 

2-71 

2-10? 

3-  li 

3-  4| 

3-7J 

3-101 

4-  2 

4-5J 

4-8* 

4-111 

5-24 

5-5! 

5-8! 

5-1  H 

25 

26 

2-5J 

2-8J 

2-11! 

3-  3 

3-6} 

3-9i 

4-0! 

4-  4 

4-7i 

4-1QJ 

5-  H 

5-5 

5-8i 

5-11-1 

6-2J 

26 

27 

2-61 

2-9| 

3-  U 

3-4J 

3-71 

3-11J 

4-2| 

4-6 

4-ej 

5-Oi 

5-4J- 

5-7i 

5-103 

6-2} 

6-5! 

27 

28 

2-  74 

2-11 

3-2i 

3-  6 

3-9^ 

,4-  1 

4-4i 

4-8 

4-ll-i 

5-3 

5-6J 

5-10 

6-  li 

6-5 

6-81 

28 

29 

2-8! 

3-Oi 

3-31 

3-7; 

3-11^ 

4-2| 

4-6| 

4-10 

5-l| 

5-5J 

5-8} 

6-04 

6-4J 

6-7! 

6-llf 

29 

30 

2-9| 

3-  li 

3-5i 

3-9 

4-0| 

4-41 

4-81 

5-0 

5-3| 

5-7i 

5-1  1* 

6-  3 

"6-6! 

6-10^ 

7-2i 

30 

8 

§ 

*£ 

If 

*i 

H 

^f 

*l 

2 

2i 

*i 

«f 

21 

2i 

2f 

21 

B 

J 

PITCH  IN  INCHES 

& 

STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE  28. 
TABLE  FOR  RIVET  SPACING. 


o 

PITCH  IN  INCHES 

jj 

2 

3 

3i 

3i 

3| 

3} 

3* 

4 

*$ 

4i 

4* 

5 

31 

at 

5$ 

0 

% 

1 

1 

2 

-6 

-6i 

-6i 

-6} 

-7 

-7i 

-8 

-8 

-0 

-9 

-10 

-10 

•u 

-11- 

1-0 

2 

3 

-9 

-91 

-9i 

-10* 

-10  £ 

-lli 

1-0 

1-0 

1-  1 

1-2 

1-3 

1-3 

1-4 

1-5 

1-6 

3 

4 

1-0 

1-OJ 

1-  1 

Mi 

1-2 

1-  3 

1-4 

1-5 

1-6 

1-7 

1-8 

1-9 

1-10 

1-11 

2-0 

4 

6 

1-3 

1-3S 

l-4i 

1-45 

1-5* 

1-61 

1-8 

l-9i 

'1-10 

1-11 

2-  1 

2-2 

2-3 

2-4 

2-6 

5 

e 

1-6 

1-6J 

l-7i 

l-8i 

1-9 

1-lOi 

2-0 

2-14 

2-3 

2-4 

2-6 

2-7 

2-9 

2-10 

3-0 

G 

7 

1-9 

i-9i 

1-10* 

Ml* 

2-04 

2-2J 

2-4 

2-5J 

2-7, 

2-9, 

2-11 

3-0 

3-2 

3-4 

3-6 

7 

8 

2-0 

2-1 

2-2 

2-3 

2-4 

2-6 

2-8 

2-10 

3-0 

3-2 

3-4 

3-6 

3-8 

3-10 

4O 

8 

9 

2-3 

2-4i 

2-5i 

2-6| 

2-7| 

2-9} 

3-0 

3-24- 

3-4j 

3-6 

3-9 

3-11 

4-  14 

4-  3 

4-6 

9 

1O 

2-6 

2-7i 

2-8J 

2-9! 

2-11 

3-  U 

3-4 

3-6J 

3-9 

3-11* 

4-2 

4-  4 

4-7 

4-  9 

5-0 

10 

11 

2-9 

2-lOi 

2-1H 

3-H 

3-2* 

3-5J 

3-8 

3-101 

4-  1- 

4-4. 

4-7 

4-9 

5-0 

5-3 

5-6 

11 

12 

3-0 

3-14 

3-3 

3-44 

3-6 

3-9 

4-0 

4-3 

4-6 

4-9 

6-0 

5-3 

5-6 

5-9 

6-0 

12 

13 

3-3 

3-4J 

3-  6| 

3-75 

3-9* 

4-0} 

4-4 

4-71 

4-10, 

5-  11 

5-5 

5-8 

5-114 

6-24 

6-6 

13 

14 

3-6 

3-7i 

3-94 

3-lli 

4-  1 

4-4J 

4-8 

4-1  H 

5-3 

5-6J 

5-10 

6-  1, 

6-  5 

6-8* 

7-0 

14 

15 

3-9 

3-10J 

4-01 

4-2£ 

4-4i 

4-8i 

5-0 

5-  3f 

5-7J 

5-lli 

6-3 

6-6, 

6-10, 

7-  2i 

7-6 

15 

16 

4-0 

4-2 

4-4 

4-6 

4-8 

5-  0 

5-4 

5-8 

6-  0 

6-4 

6-8 

7-0 

7-4 

7-8 

8-0 

16 

17 

4-3 

4-5| 

4-7* 

4-9J 

4-114 

5-3J 

5-8 

6-Oi 

6-  4^ 

6-8J 

7-  1 

7-51 

7-9i 

8-  U 

8-6 

17 

18 

4-6 

4-8J 

4-10i 

5-OJ 

5-3 

5-74 

6-0 

6-4J 

6-9 

7-  14 

7-6 

7-lOj 

8-3 

8-7-; 

9-0 

IS 

19 

4-9 

4-ll| 

5-  li 

5-4^ 

5-64 

5-lli 

6-4 

6-8J 

7-  li 

7-6i 

7-11 

8-3! 

8-8J 

9-  lj 

9-6 

19 

20 

5^0 

5-2i 

5-5 

5-74 

5-10 

6-  3 

6-8 

7-1 

7-6 

7-11 

8-4 

8-9 

9-2 

9-7 

10-0 

20 

21 

5-3 

5-5{ 

5-8i 

5-10J 

6-  14 

6-6J 

7-0 

7-5i 

7-104 

8-3J 

8-9 

9-  2i 

9-7j 

10-  Oj 

10-6 

21 

22 

5-6 

5-8^ 

5-lli 

6-21 

6-5 

6-10i 

7-4 

7-9i 

8-3 

8-8i 

9-2 

9-74 

10-  1 

10-  6J 

11-0 

22 

23 

5-9 

5-11$ 

6-2| 

6-5f 

6-84 

7-2i 

7-8 

8-11 

8-74 

9-li 

9-7 

10-  0! 

10-  6i 

11-  Oi 

11-6 

23 

24 

6-0 

6-3 

6-6 

6-9 

7-0 

7-6 

8-0 

8-6 

9-0 

9-6 

10-0 

10-6 

11-0 

11-6 

12-0 

24 

25 

6-3 

6-6* 

6-  9V 

7-Oi 

7-3i 

7-9J 

8-4 

8-10J 

9-  4| 

9-10| 

10-5 

10-1  li 

1-5} 

11-11J 

12-6 

25 

20 

6-6 

6-9i 

7-Oi 

7-3} 

7-  7 

8-  H 

8-8 

9-  24 

9-9 

0-34 

10-10 

11-  41 

11-11 

12-  5J 

13-0 

26 

27 

6-9 

7-0| 

7-3J 

7-7^ 

7-104 

8-5* 

9-0 

9-61 

10-  .14 

0-8i 

11-3 

1-91 

2-4J 

12-1  U 

13-6 

27 

28 

7-0 

7-3J 

7-7 

7-104 

8-2 

8-9 

9-4 

9-11 

0-6 

11-  1 

11-8 

2-3 

2-10 

13-5 

14-0 

28 

29 

7-3 

7-6| 

7-10J 

8-1J 

8-54 

9-  Of 

9-8 

tO-3i 

0-104 

1-51 

12-  1 

2-8J 

3-  3-i 

3-10  J 

14-6 

29 

30 

7-6 

7-91 

8-  U 

B-5J 

8-9 

9-4i 

10-0 

10-  7i 

1-  3 

1-105 

12-6 

3-  li 

3-9 

4-  4-i 

15-0 

30 

\ 

3 

3i 

31 

3| 

3'* 

3| 

4 

4>f 

4i 

41 

5 

Sj 

ffi 

5| 

6 

e 

PITCH  IN  INCHES 

I 

TABLE   29. 


TIE  RODS 


UPPER  FIGURES  IN  TABLE  GIVE 
LENGTHS  IN  FEET  AND  INCHES. 

Lower  figures  give  weights  In 
pounds  of  one  rod  and  two 
nuts. 


LENGTHS  AND  WEIGHTS  OF 

FOR  DIFFERENT  DISTANCES  CENTER  TO 

%"  TIE 

CENTER 

RODS 

OF  BEAMS 

FEET 

O" 

1  "2"3" 

4"5//6"  |7//8//9// 

1  O"  1  1  " 

1 

2 

u 

2-6 
4.5 

2:9 
4.9 

2-0 
3.8 
3-0 
5.3 

2-3 
4.2 

3 

4 

3-3 
5.7 
4-3 
7.2 

3-6 
6.O 
4-6 
7.5 

3-9 
6.4 

A   .  Q 

7  Q 

4-0 
6.8 
5-0 
8.3 

4-3 
7.2 
5-3 
8.7 

5 
6 

6-3 
1O.2 

5-6 
9.0 
6-6 
1O.5 

5-9 
9.4 
6-9 
1O.9 

6-0 
9.8 
7-0 
1  1.3 

6-3 
10.2 
7-3 
11.7 

7 
S 

7-3 
1  1.7 
8-3 
13.2 

7-6 
12.O 
8-6 
13.5 

7-9 
12.4 

8-9 
13.9 

8-0 
12.8 
9-0 
14.3 

8-3 
13.2 
9-3 
14.7 

SWEDGE  '  BOLT 


DIAMETER 

INCHES 

LENGTH- 
FEET  4  INS. 

WEIGHT 
INCLUDING    NUT 

POUNDS 

% 

0-9 

2 

7/8 

1-0 

3 

1 

1-0 

4 

Hi 

1-3 

7 

Punch  holes  W  larger  than  diameter 
of  bolt. 


BUILT-IN  ANCHOR  BOLTS 


DIAMETER 

LENGTH          WAS. 

.,,._„      WEIGHT  EACH  WITH 
•"•**         NUT  AND  WASHER 

POUNDS 

% 

2-0            4x- 

M4                   6 

% 

2-6            4  x  - 

U4 

1 

3-0            6  x  |  x  6                  14 

iy* 

4-0            6  x  - 

M6                 24 

When  center  to  center  of  anchors  is  less 
than  width  of  washer,  use  washer  with  two 
holes. 


GOVERNMENT  ANCHOR 


f 


f'  Rod    1'-9"  long    Weight  3  pounds 


ANGLE  ANCHOR 


1  Angles  6"x6"x  TV'-0'-3"  and  two  J"  bolts. 
Weight  with  bolts  10  pounds. 


STRUCTURAL   DRAWINGS,  ESTIMATES    AND   DESIGNS. 


TABLE  30. 

CHANNEL  COLUMNS. 


T's 


W      <o 


4L 


|6" 


^"CHANNEL  COLUMNS 
withl6"&l8"Cov.Pls. 


^ 

=^v'i 
il 


4'1 4" 


J 

'* 


I2CHANNEL  COLUMNS 
w!thl4"<5<l6"Cov.Pb. 


JO 

Q_ 
>: 


iOChANNEL  COLUMNS 
withl2"5l4"Cov.Pl5. 


w 


J 


ii 


' 


jn 
Q_ 

>i 


9CHANNEL  COLUMNS 


i1  10"  :: 


8CHANNEL  COLUMNS 


fe-^r 

j    Constant  ! 

JC  (Constant)! 


PLATE  &  ANGLE 
COLUMNS 


THE  DESIGN  OF 
MINE  STRUCTURES 

By  MILO  S.  KETCHUM,  C.E.,  M.AM.Soc.C.E. 

Dean  of  College  of  Engineering  and  Professor  of  Civil  Engineering, 
University  of  Colorado  ;  Consulting  Engineer 

Cloth,  6^/2x9  inches,  pp.  460+ xvi,  65  tables,  265  illustrations  in  the 
text  and  7  folding  plates.     Price,  $4.00  net,  postpaid 

TABLE   OF   CONTENTS 

PART  I.— Design  of  Head  Works.  Chapter  I.  Types  of  Head  Works.  II. 
Hoisting  from  Mines.  III.  Stresses  in  Simple  Head  Frames.  IV.  Stresses  in 
Statically  Indeterminate  Structures.  V.  Stresses  in  Statically  Indeterminate 
Head  Frames.  VI.  The  Design  of  Head  Frames.  VII.  The  Design  of  Coal 
Tipples. 

PART  n. — The  Design  of  Mine  Buildings.  Chapter  VIII.  Stresses  in  Roof 
Trusses  and  Frame  Structures.  IX.  The  Design  of  Roof  Trusses  and  Steel  Frame 
Structures.  X.  The  Design  of  Bins  and  Retaining  Walls.  XI.  The  Design  of 
Coal  Washers.  XII.  The  Design  of  Coal  Breakers.  XIII.  Miscellaneous  Struc- 
tures. 

PART  HI. — Details  of  Design  and  Cost  of  Mine  Structures.  Chapter  XIV. 
Details  of  the  Design  of  Steel  Structures.  XV.  Estimate  of  Weight  and  Cost  of 
Mine  Structures. 

APPENDIX  I.  —  Specifications  for  Steel  Mine  Structures.  Part  I.  Steel 
Frame  Buildings.  Part  II.  Steel  Head  Frames  and  Coal  Tipples,  Washers  and 
Breakers. 

APPENDIX  n.— Specifications  for  Timber  Mine  Structures. 

APPENDIX  III.— Reinforced  Concrete  Structures.  Chapter  L  Data  for  the 
Design  of  Reinforced  Concrete  Structures.  II.  Formulas  for  the  Design  of  Re- 
inforced Concrete  Structures.  III.  Specifications  for  Plain  and  Reinforced  Con- 
crete Structures. 

COMMENTS  OF  THE  PRESS 

It  is  a  pleasure  to  record  the  publication  of  another  book  by  Professor  Ketchum. 
His  books  are  always  examples  of  what  technical  treatises  should  be,  and  this  volume 
is  no  exception  to  the  rule.  This  volume  is  a  self-contained,  concise  and  valuable  text- 
book for  the  student  or  structural  engineer  who  wishes  to  become  familiar  with  the 
design  of  mine  structures. — Canadian  Engineer,  July  4,  1912. 

This  is  a  new  book  in  a  field  never  previously  covered  in  a  satisfactory  manner. 
The  various  subjects  described  and  illustrated  are  based  on  good  practical  working 
plants  and  make  them  particularly  valuable  for  reference.  The  author  is  to  be  highly 
commended  for  producing  so  useful  a  book. — Mining  and  Scientific  Press,  July  6,  1912. 

So  far  as  we  are  aware  this  book  has  no  counterpart  in  recent  technical  literature. 

— Mines  and  Minerals,  July,  1912. 


McGraw-Hill  Book  Company,  New  York 


DESIGN   OF  WALLS,  BINS 
AND   GRAIN  ELEVATORS 

SECOND  EDITION,  ENLARGED 

By  MILO  S.  KETCHUM,  C.E.,  M.AM.Soc.C.E. 

Dean  of  College  of  Engineering  and  Professor  of  Civil  Engineering, 
University  of  Colorado  ;  Consulting  Engineer 

Cloth,  6^x9  ins.,  pp.  556+xix,  40  tables,  304  illustrations  and 
2  folding  plates.     Price,  $4.00  net,  postpaid. 

TABLE  OF  CONTENTS 

PART  I. — Design  of  Retaining  Walls.  Chapter  I.  Rankine's  Theory.  I  A.  Rankine's 
Theory  Modified.  II.  Coulomb's  Theory.  III.  Design  of  Masonry  Retaining  Walls. 
IV.  Design  of  Reinforced  Concrete  Retaining  Walls.  IVA.  Effect  of  Cohesion;  Stresses 
in  Bracing  of  Trenches;  Stresses  in  Tunnels.  V.  Experiments  on  Retaining  Walls.  VI. 
Examples  of  Retaining  Walls.  VII.  Methods  of  Construction  and  Cost  of  Retaining  Walls. 

PART  II.— The  Design  of  Coal  Bins,  Ore  Bins,  etc.  Chapter  VIII.  Types  of  Coal 
Bins,  Ore  Bins,  etc.  IX.  Stresses  in  Bins.  X.  Experiments  on  Pressure  on  Bin  Walls. 
XI.  The  Design  of  Bins.  XII.  Examples  and  Details  of  Bins.  XIII.  Cost  of  Bins. 
XIV.  Methods  of  Handling  Materials. 

PART  III. — Design  of  Grain  Bins  and  Elevators.  Chapter  XV.  Types  of  Grain  Ele- 
vators. XVI.  Stresses  in  Grain  Bins.  XVII.  Experiments  on  the  Pressure  of  Grain  in 
Deep  Bins.  XVIII.  The  Design  of  Grain  Bins  and  Elevators.  XIX.  Examples  of  Grain 
Elevators.  XX.  Cost  of  Grain  Bins  and  Elevators. 

APPENDIX  I. — Concrete,  Plain  and  Reinforced.  Chapter  I.  Concrete.  II.  Data 
for  Design  of  Reinforced  Concrete  Structures.  III.  Formulas  for  Design  of  Reinforced 
Concrete.  IV.  Specifications  for  Reinforced  Concrete  Construction. 

APPENDIX  II.     Definitions  of  Masonry  Terms;  Specifications  for  Stone  Masonry. 

APPENDIX  III.     Specifications  for  Material  and  Workmanship  of  Steel  Structures. 

COMMENTS  OF  THE  PRESS. 

Those  familiar  with  Professor  Ketchum's  book  on  Steel  Mill  Buildings  will  welcome 
this  pioneer  treatise  on  bin  design,  which  is  characterized  by  the  same  thoroughness,  clear- 
ness and  logical  and  systematic  arrangement  displayed  in  the  former  volume.  ...  A 
valuable  feature  of  the  book  is  to  be  found  in  the  tables  of  costs  of  actual  structures  which 
are  included  wherever  possible  and  analyzed  so  thoroughly  as  to  be  of  the  greatest  assistance 
and  value.  For  practical  data  and  scientific  and  theoretical  accuracy,  Prof.  Ketchum's 
book  can  be  recommended  to  the  student  and  practicing  engineer  alike. —  The  Engineering 
Magazine,  November,  1907. 

This  book  will  be  welcomed  by  the  constructing  engineer  as  the  first  authoritative 
and  elaborate  contribution  to  technical  literature  on  the  perplexing  subject  of  the  design 
and  construction  of  coal  and  ore  bins.  .  .  .  The  portion  of  the  book  which  relates  to 
coal  and  ore  bins  is  the  largest,  and  this  will  make  it  appeal  especially  to  mining  and  metal- 
lurgical engineers.  They  will  find  the  admirable  study  of  retaining  walls  to  be  scarcely 
less  useful. 

Professor  Ketchum  is  well  known  as  the  author  of  "The  Design  of  Steel  Mill  Build- 
ings," which  won  high  appreciation  because  of  its  eminently  practical  character.  His 
present  work  is  one  of  the  same  order,  and  will  take  a  high  place. —  The  Engineering  and 
Mining  Journal,  June  8,  1907. 


McGraw-Hill  Book  Company,  New  York 


THE  DESIGN  OF 
HIGHWAY  BRIDGES 

AND  THE  CALCULATION  OF 
STRESSES  IN  BRIDGE  TRUSSES 


By  MILO  S.  KETCHUM,  C.E.,  M.AM.Soc.C.E. 

Dean  of  College  of  Engineering  and  Professor  of  Civil  Engineering, 
University  of  Colorado  ;  Consulting  Engineer 

Cloth,  6^x9  ins.,  pp.  544+xvi,  77  tables,  300  illustrations  in  the  text 
and  8  folding  plates.     Price,  $4.00  net,  postpaid. 

TABLE  OF  CONTENTS 

PART  I. — Stresses  in  Steel  Bridges.  Chapter  I.  Types  of  Steel  Bridges.  II.  Loads 
and  Weights  of  Highway  Bridges.  III.  Methods  for  the  Calculation  of  Stresses  in  Framed 
Structures.  IV.  Stresses  in  Beams.  V.  Stresses  in  Highway  Bridge  Trusses.  VI. 
Stresses  in  Railway  Bridge  Trusses.  VII.  Stresses  in  Lateral  Systems.  VIII.  Stresses 
in  Pins;  Eccentric  and  Combined  Stresses;  Deflection  of  Trusses;  Stresses  in  Rollers,  and 
Camber.  IX.  The  Solution  of  24  Problems  in  the  Calculation  of  Stresses  in  Bridge  Trusses. 

PART  II. — The  Design  of  Highway  Bridges.  Chapter  X.  Short  Span  Highway 
Bridges.  XI.  High  Truss  Steel  Highway  Bridges.  XII.  Plate  Girder  Bridges.  XIII. 
Design  of  Truss  Members,  XIV.  The  Details  of  Highway  Bridge  Members.  XV.  The 
Design  of  Abutments  and  Piers.  XVI.  Stresses  in  Solid  Masonry  Arches.  XVII.  Design 
of  Masonry  Bridges  and  Culverts.  XVIII.  The  Design  of  Timber  and  Combination 
Bridges.  XIX.  Erection,  Estimates  of  Weight  and  Cost  of  Highway  Bridges.  XX. 
General  Principles  of  Design  of  Highway  Bridges. 

PART  III. — A  Problem  in  Highway  Bridge  Details.  Calculation  of  Weight  and  Cost 
of  a  i6o-ft.  Span  Steel  Pratt  Highway  Bridge.  The  Calculation  of  the  Efficiencies  of  the 
Members  of  a  i6o-ft.  Span  Steel  Pin-connected  Highway  Bridge. 

APPENDIX  I.     General  Specifications  for  Steel  Highway  Bridges. 

COMMENTS  OF  THE  PRESS. 

Professor  Ketchum  has  done  the  profession  a  real  service  in  presenting  to  civil  en- 
gineers and  students  this  masterly  and  complete  work  on  highway  bridges.  The  author 
has  a  plain  way  of  getting  his  ideas  before  the  mind  of  the  reader. — Ernest  McCollough,  in 
The  Contractor,  Dec.  i,  1908. 

The  reputation  for  practical  book  writing  established  by  the  author  in  "The  Design 
of  Steel  Mill  Buildings"  and  "The  Design  of  WTalls,  Bins  and  Grain  Elevators"  is  upheld 
in  his  most  recent  work.  Altogether  we  do  not  know  where  bridge  designers  can  find 
elsewhere  so  much  good  practical  information  as  is  given  them  in  this  book. — Engineering 
Contracting,  Dec.  2,  1908. 

Altogether  the  work  embodies  a  fortunate  blending  of  the  rational  with  the  thoroughly 
practical. — Journal  of  the  Franklin  Institute,  Jan.,  1909. 


McGraw-Hill  Book  Company,  New  York 


SURVEYING  MANUAL 

A  MANUAL  OF  FIELD  AND  OFFICE  METHODS 
FOR  THE  USE  OF  STUDENTS  IN  SURVEYING 

THIRD  EDITION 
By  PROFESSORS  WILLIAM  D.  PENCE  AND   MILO  S.  KETCHUM 

Leather,  4^x7  ins.,  pp.  252+xii,   10  plates  and  140  illustrations  in 
the  text.     Price,  $2.00  net. 

TABLE  OF  CONTENTS 

Chapter  I.  General  Instructions.  II.  The  Chain  and  Tape.  III.  The  Compass. 
IV.  The  Level.  V.  The  Transit.  VI.  Topographic  Surveying.  VII.  Land  Surveying. 
VIII.  Railroad  Surveying.  IX.  Errors  of  Surveying.  X.  Methods  of  Computing.  XL 
Freehand  Lettering. 

COMMENTS  OF  THE  PRESS. 

The  object  of  the  authors  as  stated  in  the  preface,  is  first  "to  provide  a  simple  and 
comprehensive  text,  designed  to  anticipate,  rather  than  replace,  the  usual  elaborate 
treatise;  second,  to  bring  the  student  into  immediate  familiarity  with  approved  surveying 
methods;  third,  to  cultivate  the  student's  skill  in  the  rare  art  of  keeping  good  field  notes 
and  making  reliable  calculations." 

In  this  the  authors  have  succeeded  admirably.  As  a  pocket  guide  to  field  practice 
for  students,  probably  nothing  better  has  been  produced.  Especially  are  the  instructions 
in  regard  to  keeping  field  notes  to  be  commended.  Many  engineers  have  found  that  it 
has  taken  years  to  obtain  this  art,  so  generally  neglected  in  the  work  of  engineering  schools. 
— Journal  of  Western  Society  of  Engineers. 

The  scope  of  the  book  is  large,  and  the  various  subjects  included  are  treated  not  in  a 
descriptive  but  in  a  critical  manner.  The  book  is  well  arranged  and  is  written  in  a  clear 
concise  manner,  which  should  make  its  study  easy  and  pleasant. — Engineering  News. 

It  gives  the  student  just  the  information  he  needs.  The  book  is  a  gratifying  indication 
of  the  importance  attached  to  the  cultivation  of  habits  of  neatness  and  celerity  in  the 
authors'  methods  of  instruction. —  Engineering  Record. 


McGraw-Hill  Book  Company,  New  York 


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ST' 


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